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
$3x+1$ sequence beginning at 15	..., 70, 35, 106, 53, 160, 80, 40, 20, 10, 5, 16, 8, 4, 2, 1, ...	A033480
$3x-1$ sequence beginning at 5	5, 14, 7, 20, 10, 5, 14, 7, 20, 10, 5, 14, 7, 20, 10, 5, 14, ...	A003079
$7x-1$ 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.

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

Logarithms and twentieth powers

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

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

(See A010808 for the twentieth powers of integers).

Values for number theoretic functions with 20 as an argument

$\mu (20)$	0
$M(20)$	−3
$\pi (20)$	8
${\sigma }_1(20)$	42
${\sigma }_0(20)$	6
$\varphi (20)$	8
$\mathrm{\Omega }(20)$	3
$\omega (20)$	2
$\lambda (20)$	4	This is the Carmichael lambda function.
$\lambda (20)$	−1	This is the Liouville lambda function.
$\zeta (20)$	1.000000953962033872796113152... (see A013678).
20!	2432902008176640000
$\mathrm{\Gamma }(20)$	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 $\sqrt{-20}$ nor $\sqrt{20}$ generates an integrally closed ring.

Since $\sqrt{-20}=2\sqrt{-5}$, the form $a+b\sqrt{-20}$ (with $a$ and $b$ both integers) skips over numbers of the form $a+b\sqrt{-5}$ with $b$ odd.

This is even more acute for $\sqrt{20}=2\sqrt{5}$, since ${{𝒪}}_{\mathbb{\mathbb{Q}}(\sqrt{5})}=\mathbb{\mathbb{Z}}[\varphi ]$, which also includes numbers of the form $\frac{a}{2}+\frac{b\sqrt{5}}{2}$ (with $a$ and $b$ both odd integers).

Factorization of 20 in some quadratic integer rings

In $\mathbb{\mathbb{Z}}$, 20 has the prime factorization of 2 2 × 5. But it has different factorizations in some quadratic integer rings.

$\mathbb{\mathbb{Z}}[i]$	$(-i)(1-i{)}^2(1+i{)}^2(2+i)(1+2i)$
$\mathbb{\mathbb{Z}}[\sqrt{-2}]$	$(-1)(\sqrt{-2}{)}^{4}5$	$\mathbb{\mathbb{Z}}[\sqrt{2}]$	$(\sqrt{2}{)}^{4}5$
$\mathbb{\mathbb{Z}}[\omega ]$	2 2 × 5	$\mathbb{\mathbb{Z}}[\sqrt{3}]$	2 2 × 5
$\mathbb{\mathbb{Z}}[\sqrt{-5}]$	$(-1)2^2(\sqrt{-5}{)}^2$	$\mathbb{\mathbb{Z}}[\varphi ]$	$2^2(-1+2\varphi {)}^2$
$\mathbb{\mathbb{Z}}[\sqrt{-6}]$	2 2 × 5	$\mathbb{\mathbb{Z}}[\sqrt{6}]$	$(2\pm \sqrt{6}{)}^2(1\pm \sqrt{6})$
${{𝒪}}_{\mathbb{\mathbb{Q}}(\sqrt{-7})}$	${(\frac{1}{2}-\frac{\sqrt{-7}}{2})}^2{(\frac{1}{2}+\frac{\sqrt{-7}}{2})}^{2}5$	$\mathbb{\mathbb{Z}}[\sqrt{7}]$	$(3-\sqrt{7}{)}^2(3+\sqrt{7}{)}^{2}5$
$\mathbb{\mathbb{Z}}[\sqrt{-10}]$	2 2 × 5	$\mathbb{\mathbb{Z}}[\sqrt{10}]$	2 2 × 5
${{𝒪}}_{\mathbb{\mathbb{Q}}(\sqrt{-11})}$		$\mathbb{\mathbb{Z}}[\sqrt{11}]$	$(3\pm \sqrt{11}{)}^2(7\pm 2\sqrt{11})$
$\mathbb{\mathbb{Z}}[\sqrt{-13}]$		${{𝒪}}_{\mathbb{\mathbb{Q}}(\sqrt{13})}$	2 2 × 5
$\mathbb{\mathbb{Z}}[\sqrt{-14}]$		$\mathbb{\mathbb{Z}}[\sqrt{14}]$	$(-1)(4\pm \sqrt{14}{)}^2(3\pm \sqrt{14})$
${{𝒪}}_{\mathbb{\mathbb{Q}}(\sqrt{-15})}$		$\mathbb{\mathbb{Z}}[\sqrt{15}]$	2 2 × 5 OR $2(5-\sqrt{15})(5+\sqrt{15})$
$\mathbb{\mathbb{Z}}[\sqrt{-17}]$		${{𝒪}}_{\mathbb{\mathbb{Q}}(\sqrt{17})}$	${(\frac{3}{2}-\frac{\sqrt{17}}{2})}^2{(\frac{3}{2}+\frac{\sqrt{17}}{2})}^{2}5$
${{𝒪}}_{\mathbb{\mathbb{Q}}(\sqrt{-19})}$	$2^2(\frac{1}{2}-\frac{\sqrt{-19}}{2})(\frac{1}{2}+\frac{\sqrt{-19}}{2})$	$\mathbb{\mathbb{Z}}[\sqrt{19}]$	$(13\pm 3\sqrt{19}{)}^2(48\pm 11\sqrt{19})$

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

							$-1$
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