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20

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20 is an integer, the number of rooted trees with six vertices (see A000081).

Membership in core sequences

Even numbers ..., 14, 16, 18, 20, 22, 24, 26, ... A005843(10)
Composite numbers ..., 15, 16, 18, 20, 21, 22, 24, ... A002808
Oblong numbers 2, 6, 12, 20, 30, 42, 56, 72, ... A002378
Tetrahedral numbers 1, 4, 10, 20, 35, 56, 84, 120, ... A000292
Quarter-squares ..., 9, 12, 16, 20, 25, 30, 36, ... A002620
Central binomial coefficients 1, 2, 6, 20, 70, 252, 924, 3432, ... A000984

In Pascal's triangle, 20 occurs thrice, the first time in the sixth row as the sum of 10 and 10 in the row above.

Core sequences modulo 20

Integers modulo 20 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 0, 1, 2, 3, 4, ...
Prime numbers modulo 20 2, 3, 5, 7, 11, 13, 17, 19, 3, 9, 11, 17, 1, 3, 7, 13, 19, 1, 7, 11, 13, 19, 3, 9, ... A242120
Fibonacci numbers modulo 20 1, 1, 2, 3, 5, 8, 13, 1, 14, 15, 9, 4, 13, 17, 10, 7, 17, 4, 1, 5, 6, 11, 17, 8, 5, ... A287533
Squares modulo 20 1, 4, 9, 16, 5, 16, 9, 4, 1, 0, 1, 4, 9, 16, 5, 16, 9, 4, 1, 0, 1, 4, 9, 16, 5, 16, ... A070442
Powers of 2 modulo 20 1, 2, 4, 8, 16, 12, 4, 8, 16, 12, 4, 8, 16, 12, 4, 8, 16, 12, 4, 8, 16, 12, 4, 8, ...

Sequences pertaining to 20

Multiples of 20 0, 20, 40, 60, 80, 100, 120, 140, 160, 180, 200, 220, 240, ... A008602
20-gonal numbers 1, 20, 57, 112, 185, 276, 385, 512, 657, 820, 1001, 1200, ... A051872
Centered 20-gonal numbers 1, 21, 61, 121, 201, 301, 421, 561, 721, 901, 1101, 1321, ... A069133
sequence beginning at 15 ..., 70, 35, 106, 53, 160, 80, 40, 20, 10, 5, 16, 8, 4, 2, 1, ... A033480
sequence beginning at 5 5, 14, 7, 20, 10, 5, 14, 7, 20, 10, 5, 14, 7, 20, 10, 5, 14, ... A003079
sequence beginning at 3 3, 20, 10, 5, 34, 17, 118, 59, 412, 206, 103, 720, 360, ... A063871

Partitions of 20

There are 627 partitions of 20. Of these, only ten are pairs, and of those ten pairs, only two are valid Goldbach representations: 3 + 17 = 7 + 13 = 20.

Roots and powers of 20

In the table below, irrational numbers are given truncated to eight decimal places.

4.47213595 A010476 20 2 400
2.71441761 A010592 20 3 8000
2.11474252 A011016 20 4 160000
1.82056420 A011105 20 5 3200000
1.64754897 A011425 20 6 64000000
1.53412740 A011426 20 7 1280000000
1.45421543 A011427 20 8 25600000000
1.39495079 A011428 20 9 512000000000
1.34928284 A011429 20 10 10240000000000
1.31303243 A011430 20 11 204800000000000
1.28356884 A011431 20 12 4096000000000000
A009964

Logarithms and twentieth powers

In the table below, irrational numbers are given truncated to eight decimal places.

0.23137821 A152821 4.32192809 A155172 2 20 1048576
0.33380820 2.99573227 A016643
0.36672579 A153035 2.72683302 A102447 3 20 3486784401
0.38212022 2.61697742
0.46275642 A153124 2.16096404 A155183 4 20 1099511627776
0.53724357 A153454 1.86135311 A155184 5 20 95367431640625
0.59810400 A153610 1.67195001 A155490 6 20 3656158440062976
0.64956076 A153630 1.53950184 A155496 7 20 79792266297612001
0.69413463 A153872 1.44064269 A155502 8 20 1152921504606846976
0.73345158 A154019 1.36341651 A155503 9 20 12157665459056928801
0.76862178 A154170 1.30102999 A155522 10 20 100000000000000000000

(See A010808 for the twentieth powers of integers).

Values for number theoretic functions with 20 as an argument

0
−3
8
42
6
8
3
2
4 This is the Carmichael lambda function.
−1 This is the Liouville lambda function.
1.000000953962033872796113152... (see A013678).
20! 2432902008176640000
121645100408832000

Factorization of some small integers in a quadratic integer ring adjoining the square roots of −20, 20

Given that 20 is not squarefree, adjoining neither nor generates an integrally closed ring.

Since , the form (with and both integers) skips over numbers of the form with odd.

This is even more acute for , since , which also includes numbers of the form (with and both odd integers).

Factorization of 20 in some quadratic integer rings

In , 20 has the prime factorization of 2 2 × 5. But it has different factorizations in some quadratic integer rings.

2 2 × 5 2 2 × 5
2 2 × 5
2 2 × 5 2 2 × 5
2 2 × 5
2 2 × 5 OR

Representation of 20 in various bases

Base 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
Representation 10100 202 110 40 32 26 24 22 20 19 18 17 16 15 14 13 12 11 10

20 is a Harshad number in every base from binary to decimal except for bases 7 and 8.

See also

Some integers
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