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45
From OeisWiki
45 is an integer.
Contents
- 1 Membership in core sequences
- 2 Sequences pertaining to 45
- 3 Partitions of 45
- 4 Roots and powers of 45
- 5 Logarithms and 45th powers
- 6 Values for number theoretic functions with 45 as an argument
- 7 Factorization of some small integers in a quadratic integer ring adjoining the square roots of −45, 45
- 8 Factorization of 45 in some quadratic integer rings
- 9 Representation of 45 in various bases
- 10 See also
Membership in core sequences
Odd numbers | ..., 39, 41, 43, 45, 47, 49, 51, ... | A005408 |
Composite numbers | ..., 40, 42, 44, 45, 46, 48, 49, ... | A002808 |
Triangular numbers | ..., 21, 28, 36, 45, 55, 66, 78, ... | A000217 |
Little Schroeder numbers | 1, 1, 3, 11, 45, 197, 903, 4279, ... | A001003 |
Numbers that are the sum of two squares | ..., 37, 40, 41, 45, 49, 50, 52, ... | A001481 |
Like all triangular numbers, 45 occurs more than twice in Pascal's triangle, specifically, 45 occurs four times.
Sequences pertaining to 45
Multiples of 45 | 0, 45, 90, 135, 180, 225, 270, 315, 360, 405, ... |
Partitions of 45
There are 89134 partitions of 45.
The Goldbach representations of 45 using distinct primes are: 43 + 2 = 37 + 5 + 3 = 31 + 11 + 3 = 29 + 13 + 3 = 29 + 11 + 5 = 23 + 19 + 3 = 23 + 17 + 5 = 45.
Roots and powers of 45
In the table below, irrational numbers are given truncated to eight decimal places.
TABLE GOES HERE
Logarithms and 45th powers
REMARKS
TABLE
Values for number theoretic functions with 45 as an argument
TABLE GOES HERE
Factorization of some small integers in a quadratic integer ring adjoining the square roots of −45, 45
Since 45 is not squarefree, [FINISH WRITING]
Factorization of 45 in some quadratic integer rings
PLACEHOLDER
TABLE GOES HERE
Representation of 45 in various bases
Base | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 |
Representation | 101101 | 1200 | 231 | 140 | 113 | 63 | 55 | 50 | 45 | 41 | 39 | 36 | 33 | 30 | 2D | 2B | 29 | 27 | 25 |
The square of 45 is 2025. Notice that 20 + 25 = 45. This means that 45 is a base 10 Kaprekar number (see A006886).
See also
0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 |
20 | 21 | 22 | 23 | 24 | 25 | 26 | 27 | 28 | 29 |
30 | 31 | 32 | 33 | 34 | 35 | 36 | 37 | 38 | 39 |
40 | 41 | 42 | 43 | 44 | 45 | 46 | 47 | 48 | 49 |
1729 |