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# Annotated version of "What's Special About This Number?" (Part 5)

## Introduction

Erich Friedman has a very nice (and deservedly popular) page called
**What's Special About This Number?**

It does not, however, mention the sequences in the OEIS where these numbers can be found (and from where I suspect most of the entries were taken).

The present set of ten pages is a snapshot of his page as of May 23, 2010, with pointers to the corresponding entries in the OEIS. The pages are:

- Part 0: 0 to 999,
- Part 1: 1000 to 1999,
- Part 2: 2000 to 2999,
- Part 3: 3000 to 3999,
- Part 4: 4000 to 4999,
- Part 5: 5000 to 5999,
- Part 6: 6000 to 6999,
- Part 7: 7000 to 7999,
- Part 8: 8000 to 8999,
- Part 9: 9000 to 9999.

People are invited to add more pointers to these pages, by adding the appropriate A-numbers to the entries. It may be necessary to create new sequences to do this - see A158304 for an example.

I should add that this is being done with Erich Friedman's approval.

I did not do a very good job of converting the original html format to wiki format, and in some cases you may have to refer to Erich's page to figure out the meaning or the links.

You may well find better descriptions for some numbers. If so, please send them to Erich and make the corresponding changes here. (The wiki software is complaining that these pages are too long. I decided to ignore these complaints.)

Neil Sloane

## Part 5: The Numbers 5000 to 5999

**5000** is the largest number whose English name does not repeat any letters

**5001** appears inside its 4^{th} power

**5002** has a 4^{th} power containing only 4 different digits

**5005** is the smallest palindromic product of 4 consecutive primes

**5009** would be prime if preceded and followed by a 1, 3, 7, or 9

**5010** has a square with the last 3 digits the same as the 3 digits before that

**5016** is a heptagonal pyramidal number

**5020** is an amicable number

**5024** is a member of the Fibonacci -type sequence starting with 2 and 7

**5026** is the number of connected graphs with 11 vertices and 1 cycle

**5030** is the closest integer to 23^{e }

**5036** and the two numbers before it and after it are all products of exactly 3 primes

**5039** is the number of planar partitions of 18

**5040** = 7!

**5041** is the largest square known of the form n! + 1

**5042** is the number of subsets of {1,2,3,...,16} that have a sum divisible by 13

**5044** is a value of n for which φ (n) and σ (n) are square

**5046** is the first of five consecutive squareful numbers

**5048** is the number of strongly connected digraphs with 5 vertices

**5049** is an octagonal pyramidal number (A002414)

**5050** is the sum of the first 100 integers (A000217)

**5054** = 555 + 0 + 55 + 4444

**5055** has exactly the same digits in 3 different bases

**5056** is the number of ways to flip a coin 13 times and get at least 3 heads in a row

**5057** is the number of squares in a 16×16 grid of squares with diagonals drawn

**5059** is the number of inequivalent asymmetric Ferrers graphs with 33 points

**5061** is a number n whose 5^{th} root has a decimal part that begins with the digits of n

**5069** is the number of square-free graphs with 10 vertices

**5071** is a Lucas 3-step number and a Lucas 4-step number

**5077** has a square whose digits each occur twice

**5078** is the number of rectangles with corners on an 12×12 grid of points

**5080** is a structured truncated octahedral number

**5083** is an centered icosahedral number

**5084** is the number of inequivalent Ferrers graphs with 33 points

**5087** has an eleventh root whose decimal part starts with the digits 1-9 in some order

**5088** divides the sum of the digits of 2^{5088} × 5088!

**5096** is the number of possible rook moves on a 14×14 chessboard

**5098** is the number of 3-valent trees with 17 vertices

**5100** is divisible by its reverse

**5103** and its successor are both divisible by 4^{th} powers

**5104** is the smallest number that can be written as the sum of 3 cubes in 3 ways

**5105** would be prime if preceded and followed by a 1, 3, 7, or 9

**5107** preceded by 5107 1's is prime

**5108** is the number of different flushes in 5 card poker

**5109** is the number of conjugacy classes of the alternating group A_{33}

**5118** is the maximum value of n so that there exist 6 denominations of stamps so that every postage from 1 to n can be paid for with at most 12 stamps

**5120** is the number of edges in a 10 dimensional hypercube

**5130** is a value of n for which φ (n) and σ (n) are square

**5133** is the smallest integer ratio of a 18-digit number to its product of digits

**5134** has the property that the sum of the factorials of its digits is its largest prime factor

**5135** is not the sum of a square , a cube , a 4^{th} power, and a 5^{th} power

**5136** does not occur in its factorial in base 2

**5141** is the sum of the first 17 numbers that have digit sum 17

**5141** is the only four digit number that is reversed in hexadecimal

**5142** is the sum of its proper divisors that contain the digit 7

**5143** = 555 + 111 + 4444 + 33

**5146** has a base 3 representation that begins with its base 7 representation

**5152** is the number of legal rook moves in Chess

**5153** is an Eisenstein-Mersenne prime (A066408)

**5160** is a hendecagonal pyramidal number

**5161** = 5! + (1+6)! + 1!

**5162** = 5! + (1+6)! + 2

**5163** = 5! + (1+6)! + 3

**5164** = 5! + (1+6)! + 4

**5165** = 5! + (1+6)! + 5

**5166** = 5! + (1+6)! + 6

**5167** = 5! + (1+6)! + 7

**5168** has a square root that has four 8's immediately after the decimal point

**5169** = 5! + (1+6)! + 9

**5172** has a cube whose last few digits are ...48848448

**5174** has a 4^{th} power containing only 4 different digits

**5176** is the number of labeled graphs with 6 vertices that have chromatic number 2

**5177** is the number of labeled bipartite graphs with 6 vertices

**5180** is the smallest number whose 7^{th} power has 26 digits

**5181** is a structured octagonal anti-diamond number

**5182** is a number whose sum of divisors is a 5^{th} power

**5183** is the product of twin primes

**5184** is the number of ways to place 2 non-attacking rooks on a 9×9 chessboard

**5185** is the number of 2×2 singular matrices mod 17

**5186** is equal to the sum of its anti-divisors

**5187** is the only number n known for which φ (n-1) = φ (n) = φ (n+1)

**5191** is a value of n for which σ (n+1) = 2σ (n)

**5199** divides the sum of the cubes of the first 5199 primes

**5200** is divisible by its reverse

**5204** has the property that if each digit is replaced by its square , the resulting number is a square

**5211** has a square root whose decimal part starts with the digits 1-9 in some order

**5216** is a structured hexagonal diamond number

**5218** is the number of 3-colorable graphs connected graphs with 8 vertices

**5220** = 1111 in base 17

**5222** has the property that the sum of the n^{th} powers of its digits is prime for 1 ≤ n &\le 9

**5225** is the number of ways to color the vertices of a triangle with 25 colors, up to rotation

**5226** is the number of ways to color the vertices of a square with 12 colors, up to rotation

**5229** uses the same digits as φ (5229)

**5234** has a cube that is only 17 away from a square

**5237** is a value of n for which n and 8n together use each digit 1-9 exactly once

**5239** has a square whose digits each occur twice

**5241** is the starting location of 7777 in the decimal expansion of π

**5242** is the number of ways to place 8 non-attacking kings on a 8×8 chessboard so that there is a king in every row and column

**5244** is the sum of consecutive squares in 2 ways

**5247** is the number of ordered ways to write 1 as a sum of reciprocals of integers no larger than 10

**5248** is the number of ordered ways to write 1 as a sum of reciprocals of integers no larger than 11

**5250** is the number of linear geometries on 10 unlabeled points

**5252** is the maximum number of regions space can be divided into by 26 spheres

**5256** is the number of labeled partially ordered sets of 4 elements

**5257** is a member of the Fibonacci -type sequence starting with 1 and 8

**5258** has a base 8 representation which is the reverse of its base 7 representation

**5260** is the number of multigraphs with 24 vertices and 4 edges

**5264** is the smallest number so that it and its successor are both the product of 2 primes and the 4^{th} power of a prime

**5265** is a Rhonda number

**5269** is the number of binary rooted trees with 18 vertices

**5271** is a value of n for which 2n and 7n together use each digit exactly once

**5274** is the sum of its proper divisors that contain the digit 7

**5278** is the number of ways, up to symmetry, to pick 3 elements of an 8×8 grid

**5279** is the number permutations of {1,2,3,...,20} where adjacent numbers differ by no more than 2

**5280** is the number of feet in a mile

**5281** has a 4^{th} power that is the sum of four 4^{th} powers

**5282** is the number of different arrangements (up to rotation and reflection) of 8 non-attacking rooks on a 8×8 chessboard

**5284** and the two numbers before it and after it are all products of exactly 3 primes

**5289** is a structured rhombic triacontahedral number

**5291** is a value of n for which n(n+1) is a palindrome .

**5292** = 28 + 0 + 0 + 5264 and has square 28005264

**5293** is the smallest number that ends an arithmetic progression of 12 numbers with the same prime signature

**5296** is the Entringer number E(8,3).

**5306** is the smallest number whose 9^{th} power starts with 4 identical digits

**5309** has the property that if each digit is replaced by its square , the resulting number is a square

**5312** is the index of a prime Woodall number

**5313** is the index of a triangular number containing only 3 different digits

**5314** is a value of n for which |cos(n)| is smaller than any previous integer

**5322** is the starting location of 7777 in the decimal expansion of π

**5324** is the number of binary cube-free words of length 20

**5327** is a value of n for which 2n and 7n together use each digit exactly once

**5328** is the number of one-sided 6-knights

**5332** is a Kaprekar constant in base 3

**5335** is the magic constant of a 22×22 magic square

**5336** is a house number

**5340** is an octahedral number

**5346** = 198 × 27 and each digit is contained in the equation exactly once

**5349** = 12345 in base 8

**5355** is an odd primitive abundant number (A091191, A006038)

**5357** is the smallest number that can not be formed using the digit 1 at most 27 times, together with the symbols +, –, × and ÷

**5358** are the first 8 digits of π ^{5358}

**5362** is the number of Chess positions that can be reached after 2 moves by white and 1 move by black

**5364** is a value of n for which 3n and 7n together use each digit exactly once

**5366** is the number of graphs with 8 vertices that have chromatic number 4

**5367** uses the same digits as φ (5367)

**5369** is a Wolstenholme number

**5371** is a value of n for which n and 8n together use each digit 1-9 exactly once

**5376** is the order of a perfect group

**5382** is the number of non-intersecting rook paths joining opposite corners of a 6×4 chessboard

**5383** is the number of triangles of any size contained in the triangle of side 27 on a triangular grid

**5387** is the index of a prime Fibonacci number

**5390** is the number of ways to 7-color the faces of a cube

**5392** is a Leyland number

**5399** has a cube whose digits occur with the same frequency

**5400** is divisible by its reverse

**5401** is a member of the Fibonacci -type sequence starting with 3 and 7

**5405** is the smaller number in a Ruth-Aaron pair

**5406** is the number of ways a 9×1 rectangle can be surrounded by 9×1 rectangles

**5408** is an Achilles number

**5409** and its reverse are both differences of positive cubes

**5412** is a value of n so that n(n+4) is a palindrome

**5414** is the number of binary partitions of 43

**5418** is a value of n for which n and 7n together use each digit 1-9 exactly once

**5419** is a Cuban prime

**5422** is the number of semigroups of order 6 with 3 idempotents

**5431** is the smallest number whose 4^{th} power contains 5 consecutive 9's

**5432** has digits in arithmetic sequence

**5434** is the sum of consecutive squares in 2 ways

**5436** is the number of terms in the 10^{th} derivative of f(f(f(f(f(x)))))

**5439** is a Rhonda number

**5440** is the number of ways to legally add 2 sets of parentheses to a product of 15 variables

**5443** is the smallest prime p with 17 consecutive quadratic residues mod p

**5446** is the number of ways to to arrange the numbers 1-10 around a circle so that the sums of adjacent numbers are distinct

**5448** is the number of ways to cut a 10×10 chessboard into 2 pieces with equal areas with a cut that only travels up and right

**5455** is a Kaprekar number for cubes

**5456** and its reverse are tetrahedral numbers

**5457** is a number whose sum of divisors is a 5^{th} power

**5460** is both a triangular number and 7 times a triangular number

**5461** is a Poulet number

**5462** is the number of ways to walk along 14 edges of a triangle and end at the original vertex

**5463** has a 4^{th} power that is the sum of four 4^{th} powers

**5464** is the number of subsets of {1,2,3,...,16} that have a sum divisible by 12

**5469** has the property that e ^{5469] } is within .00003 of an integer

**5471** contains no 0's in base 3 through base 10

**5472** has a base 3 representation that ends with its base 4 representation

**5473** has a base 3 representation that ends with its base 4 representation

**5474** is a stella octangula number

**5477** and its reverse are both one more than a square

**5478** is the number of graphs with 10 vertices that have chromatic number 2

**5479** is the number of bipartite graphs with 10 vertices

**5482** is the number of 3×3 sliding puzzle positions that require exactly 16 moves to solve starting with the hole in the center

**5483** is the number of unlabeled distributive lattices with 18 elements

**5487** is the maximum number of pieces a torus can be cut into with 31 cuts

**5488** is an Achilles number

**5489** is the maximum number of regions a cube can be cut into with 32 cuts

**5491** has a 4^{th} power that is the sum of four 4^{th} powers

**5493** is the number of integers with complexity 30

**5499** is the average of all the even 4-digit numbers

**5504** is the number of series-parallel networks with 6 labeled edges

**5505** is a value of n for which n!!! - 1 is prime

**5507** has a square root whose decimal part starts with the digits 0-9 in some order

**5508** is the generalized Catalan number C(13,5)

**5509** is the number of multigraphs with 8 vertices and 9 edges

**5513** is the number of self-avoiding walks of length 10

**5525** is the smallest number that can be written as the sum of 2 squares in 6 ways

**5530** is a hexagonal pyramidal number

**5533** is the number of graphs with 10 vertices and 2 cycles

**5536** is the 16^{th} Tetranacci number

**5542** is the number of anisohedral 19-ominoes

**5543** has a 4^{th} power that is the sum of four 4^{th} powers

**5544** is the number of permutations of 9 items that fix 4 elements

**5545** is a member of the Fibonacci -type sequence starting with 1 and 5

**5551** is the number of trees on 17 vertices with diameter 6

**5554** is a Kaprekar number for cubes

**5555** is a repdigit

**5557** contains no 0's in base 3 through base 10

**5560** are the first 4 digits of 7^{5560}

**5561** has the property that the sum of its prime factors is equal to the product of its digits

**5564** is an amicable number

**5565** is a doubly triangular numbers

**5566** is a pentagonal pyramidal number

**5568** is the number of ways to put 8 checkers on an 8×8 checkerboard so that each row, column, and main diagonal contains exactly one checker

**5571** is a perfect totient number

**5573** is the number of digits in the 6^{th} Cullen prime

**5576** is a decagonal pyramidal number

**5585** is the number of monoids of order 7 with 2 idempotents

**5586** does not occur in its factorial in base 2

**5587** has a 5^{th} root that starts 5.61611166...

**5588** is the index of a triangular number containing only 3 different digits

**5591** is the smallest prime that is followed by 31 composite numbers .

**5594** is the number of ways to dissect a 14-gon using non-crossing diagonals into polygons with an even number of sides.

**5595** is the number of labeled mappings from 6 points to themselves with exactly 3 cycles.

**5597** has a cube with only odd digits.

**5600** is the number of self-complementary graphs with 13 vertices

**5602** = 22222 in base 7 [A125725)

**5604** is the number of partitions of 30

**5610** is divisible by its reverse

**5611** is the smallest number for which it and the 3 numbers before and after it all have φ (n) divisible by 10

**5612** has the property that dropping its first and last digits gives its largest prime factor

**5616** is the order of a non-cyclic simple group

**5617** is a divisor of the sum of the 4^{th} powers of its divisors

**5619** has a cube that contains the digits 5619 in reverse order

**5620** is the smallest composite number which remains composite when preceded or followed by any digit

**5623** and the primes preceding it and following it are all equal to 7 (mod 16)

**5624** is the smallest number whose 4^{th} power has 15 digits

**5625** has a cube that is the sum of 3 positive cubes

**5629** is the maximum value of n so that there exist 5 denominations of stamps so that every postage from 1 to n can be paid for with at most 16 stamps

**5637** uses the same digits as φ (5637)

**5638** is the number of 3×3 sliding puzzle positions that require exactly 17 moves to solve starting with the hole in a corner

**5647** is the closest integer to 24^{e }

**5651** is a number n for which n, n+2, n+6, and n+8 are all prime

**5661** is the trinomial coefficient T(18,14)

**5664** is a Rhonda number

**5668** is the number of semigroups of order 6 with 5 idempotents

**5669** is a value of n for which |cos(n)| is smaller than any previous integer

**5670** is a value of n for which φ (n) and σ (n) are square

**5671** is a triangular number that is the product of two primes

**5673** is the smallest number whose 6^{th} power starts with 5 identical digits

**5675** is the number of monic polynomials of degree 13 with integer coefficients whose complex roots are all in the unit disk

**5678** has digits in arithmetic sequence

**5679** is the number of drawings of the complete graph K_{10} with a minimal number of crossings

**5682** is the sum of its proper divisors that contain the digit 4

**5689** is the largest 4-digit prime with strictly increasing digits

**5691** is the number of different resistances that can be created in a circuit of 11 equal resistors

**5692** is a number that does not have any digits in common with its cube

**5693** = 5555 + 6 + 99 + 33

**5694** = 17082 / 3, and each digit is contained in the equation exactly once

**5696** is the smallest number whose square contains 4 consecutive 4's

**5697** has a 21^{st} power that contains five 5's, six 6's, nine 9's, and seven 7's

**5698** is the smallest number whose 8^{th} power starts with 5 identical digits

**5700** is divisible by its reverse

**5709** is a structured pentakis dodecahedral number

**5711** is the smallest prime p with 18 consecutive quadratic residues mod p

**5712** is the number of Gray codes for a 4-dimensional cube

**5717** is a value of n for which the first n binary digits of π form a prime

**5718** is the number of partitions of 54 into distinct parts

**5719** is a Zeisel number

**5720** is a dodecagonal pyramidal number

**5721** is the number of graphs with 8 vertices that have chromatic number 3

**5723** has the property that its square starts with its reverse

**5729** has a 4^{th} power that is the sum of four 4^{th} powers

**5731** is a value of n for which n (n+2) is a palindrome

**5734** has a square that is a centered pentagonal number

**5737** is the smallest number that can not be formed using the digit 1 at most 22 times, together with the symbols +, × and ^

**5739** is a value of n for which 5n and 7n together use each digit exactly once

**5740** = 7777 in base 9

**5741** is the 11^{th} Pell number

**5742** is a value of n for which 5n and 8n together use each digit exactly once

**5751** is the number of ordered sequences of coins totaling 31 cents

**5754** is the number of ways a loop can cross two parallel lines a total of 12 times

**5755** is the sum of the digits of the 19^{th} Mersenne prime (A066538)

**5760** is the order of a perfect group

**5767** is the product of two consecutive primes

**5768** is the 16^{th} tribonacci number

**5770** is a value of n for which φ (n) and σ (n) are square

**5772** are the first 4 decimal digits of Euler's constant

**5773** is the index of a triangular number containing only 3 different digits

**5774** is the smallest number whose square begins with four 3's

**5775** is the smallest value of n for which both n and n+1 are abundant (A096399)

**5776** is the square of the last half of its digits

**5777** is the smallest multi-digit number which is not the sum of a prime and twice a square

**5778** is the largest Lucas number which is also a triangular number

**5781** is a centered tetrahedral number

**5784** has a square whose digits each occur twice

**5786** = 5555 + 77 + 88 + 66

**5789** is a value of n for which n and 8n together use each digit 1-9 exactly once

**5790** has the same digits as the 5790^{th} prime

**5791** is a value of n for which n and 8n together use each digit 1-9 exactly once

**5793** are the first 4 digits of 5793^{e }

**5795** is a value of n such that the n^{th} Cullen number is prime

**5796** = 138 × 42 and each digit is contained in the equation exactly once

**5798** is the 11^{th} Motzkin number

**5807** is the index of a Wagstaff prime

**5813** is the concatenation of 3 consecutive Fibonacci numbers

**5814** = _{19}P _{3}

**5817** = 34902 / 6, and each digit is contained in the equation exactly once

**5818** contains no 0's in base 3 through base 10

**5819** has a sum of digits equal to its largest prime factor

**5821** contains no 0's in base 3 through base 10

**5822** is the number of conjugacy classes in the automorphism group of the 16 dimensional hypercube .

**5823** is the smallest value of n for which n and 3n together use each digit 1-9 exactly once

**5824** can be written as the difference between two positive cubes in more than one way

**5825** are the first 4 digits of e^{5825}

**5830** is a weird number

**5831** has a sum of digits equal to its largest prime factor

**5832** is a value of n for which n and 3n together use each digit 1-9 exactly once

**5834** is the number of digits of the 21^{st} perfect number [A061193)

**5839** is a value of n for which n and 8n together use each digit 1-9 exactly once

**5842** is a Padovan number

**5843** has a 5^{th} root that starts 5.66666...

**5844** is the number of ways to stack 34 boxes in a line so that each box lies on the table or on a box next to 2 boxes

**5848** has a square that remains square when a 9 is appended to it

**5850** is a value of n for which n-1 and n+1 are twin primes , and so are 2n-1 and 2n+1

**5851** is a value of n for which n, n^{2}, and n^{3} have the same digit sum

**5853** is the index of a triangular number containing only 3 different digits

**5856** = 1 × 6 × 16 × 61

**5858** has a square whose digits each occur twice

**5859** can be written as the difference between two positive cubes in more than one way

**5860** is the sum of the squares of 4 consecutive primes

**5863** is the starting location of 7777 in the decimal expansion of π

**5864** has a 14^{th} power that contains five 5's, eight 8's, six 6's, and four 4's

**5865** is an enneagonal pyramidal number

**5867** is a member of the Fibonacci -type sequence starting with 1 and 9

**5868** is a value of n for which n, n^{2}, and n^{3} have the same digit sum

**5870** has a digit sum smaller than its cube

**5872** = 5555 + 88 + 7 + 222

**5873** divides 1^{1} + 2^{2} + 3^{3} + ^{ . . .} + 5873^{5873}

**5876** is the number of ways to color the vertices of a triangle with 26 colors, up to rotation

**5877** is a value of n for which 5n and 8n, or 8n and 9n, together use each digit exactly once

**5879** is the smallest number so that it and the next 10 numbers all have an odd number of prime factors

**5880** is the Stirling number of the second kind S(10,7)

**5885** is a number whose sum of divisors is a 5^{th} power

**5886** is a value of n for which 3n and 5n together use each digit exactly once

**5890** is a heptagonal pyramidal number

**5892** is a value of n for which n and 8n together use each digit 1-9 exactly once

**5895** is the number of necklaces possible with 7 beads, each being one of 5 colors

**5896** is the number of ways to tile a 3×24 rectangle with 3×1 rectangles

**5900** is the number of ways to place 32 points on a 16×16 grid so that no 3 points are on a line

**5904** has a square comprised of the digits 1-8

**5906** is the smallest number which is the sum of 2 rational 4^{th} powers but is not the sum of two integer 4^{th} powers

**5909** is the number of symmetric plane partitions of 32

**5913** = 1! + 2! + 3! + 4! + 5! + 6! + 7!

**5914** = 0! + 1! + 2! + 3! + 4! + 5! + 6! + 7!

**5915** is the sum of consecutive squares in 2 ways

**5916** is a value of n for which n and 8n together use each digit 1-9 exactly once

**5921** is a value of n for which n and 8n together use each digit 1-9 exactly once

**5923** is the largest n so that **Q** (√n) has class number 7

**5925** is the index of a triangular number containing only 3 different digits

**5926** + φ (5926) = 8888

**5929** is a square which is also the sum of 11 consecutive squares

**5931** is the number of one-sided 7-kings

**5934** is a value of n for which 5n and 7n together use each digit exactly once

**5935** is a Smith brother

**5936** is divisible by the digits it does not contain, and not divisible by the digits it contains

**5938** is the number of binary partitions of 44

**5939** is the smallest prime so that it and the next 2 primes are all equal to 3 (mod 7)

**5940** is divisible by its reverse

**5941** is the number of interior intersections when all the diagonals of a regular 22-gon are drawn

**5943** is a value of n for which n, n+1, n+2, and n+3 have the same number of divisors

**5950** is the sum of the digits of the 20^{th} Mersenne prime (A066538)

**5953** and the primes preceding it and following it are all equal to 3 (mod 14)

**5958** is the number of subsets of {1,2,3,...,16} that have a sum divisible by 11

**5959** is the smaller number in a Ruth-Aaron pair

**5960** is the larger number in a Ruth-Aaron pair

**5963** is the number of intersections when all the diagonals of a regular 22-gon are drawn

**5967** is a value of n for which 6n and 7n together use each digit exactly once

**5968** has a square which uses the digits 0-7 each exactly once

**5972** is the smallest number that appears in its factorial 8 times

**5974** is the number of connected planar graphs with 8 vertices

**5975** is a value of n for which σ (n) = σ (reverse(n))

**5976** is a value of n for which n and 7n together use each digit 1-9 exactly once

**5978** is a value of n where φ (n) is the product of the digits of n

**5984** = _{34}C _{3}

**5985** = _{21}C _{4}

**5986** and its prime factors contain every digit from 1-9 exactly once

**5993** is the largest number known which is not the sum of a prime and twice a square

**5994** is the number of lattices on 10 unlabeled nodes

**5995** is a palindromic triangular number

**5996** is a truncated tetrahedral number

**5999** is the smallest number whose digits add to 32