90

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90 is an integer.

Membership in core sequences

Even numbers	..., 84, 86, 88, 90, 92, 94, 96, ...	A005843
Composite numbers	..., 86, 87, 88, 90, 91, 92, 93, ...	A002808
Abundant numbers	..., 80, 84, 88, 90, 96, 100, 102, ...	A005101
Oblong numbers	..., 42, 56, 72, 90, 110, 132, 156, ...	A002378
Quarter-squares	..., 64, 72, 81, 90, 100, 110, 121, ...	A002620
Numbers that are the sum of two squares	..., 82, 85, 89, 90, 97, 98, 100, ...	A001481
Large Schröder numbers	1, 2, 6, 22, 90, 394, 1806, 8558, ...	A006318

Sequences pertaining to 90

Multiples of 90	0, 90, 180, 270, 360, 450, 540, 630, ...
Divisors of 90	1, 2, 3, 5, 6, 9, 10, 15, 18, 30	A018278

Partitions of 90

There are 56634173 partitions of 90.

The Goldbach representations of 90 are: 83 + 7 = 79 + 11 = 73 + 17 = 71 + 19 = 67 + 23 = 61 + 29 = 59 + 31 = 53 + 37 = 47 + 43 = 90.

Values for number theoretic functions with 90 as an argument

PLACEHOLDER

Factorization of 90 in some quadratic integer rings

As was mentioned above, 90 is the product of four primes (three distinct) in $\mathbb {Z}$ . But in some quadratic integer rings, some of these primes are further reducible.

$\mathbb {Z} [i]$	$(1\pm i)3^{2}(2\pm i)$
$\mathbb {Z} [{\sqrt {-2}}]$	$(-1)({\sqrt {-2}})^{2}(1\pm {\sqrt {-2}})^{2}5$	$\mathbb {Z} [{\sqrt {2}}]$	$({\sqrt {2}})^{2}3^{2}\times 5$
$\mathbb {Z} [\omega ]$	$2(1+2\omega )^{4}5$	$\mathbb {Z} [{\sqrt {3}}]$	$(-1)(1\pm {\sqrt {3}})({\sqrt {3}})^{4}5$
$\mathbb {Z} [{\sqrt {-5}}]$	$(-1)2\times 3^{2}({\sqrt {-5}})^{2}$	$\mathbb {Z} [\phi ]$	$2\times 3^{2}(-1+2\phi )^{2}$
$\mathbb {Z} [{\sqrt {-6}}]$	2 × 3 2 × 5	$\mathbb {Z} [{\sqrt {6}}]$	$(2\pm {\sqrt {6}})(3\pm {\sqrt {6}})^{2}(1\pm {\sqrt {6}})$
${\mathcal {O}}_{\mathbb {Q} ({\sqrt {-7}})}$	$\left({\frac {1}{2}}\pm {\frac {\sqrt {-7}}{2}}\right)3^{2}\times 5$	$\mathbb {Z} [{\sqrt {7}}]$	$(3\pm {\sqrt {7}})(2\pm {\sqrt {7}})^{2}5$
$\mathbb {Z} [{\sqrt {-10}}]$	2 × 3 2 × 5	$\mathbb {Z} [{\sqrt {10}}]$	2 × 3 2 × 5
${\mathcal {O}}_{\mathbb {Q} ({\sqrt {-11}})}$	$2\left({\frac {1}{2}}\pm {\frac {\sqrt {-11}}{2}}\right)^{2}\left({\frac {3}{2}}\pm {\frac {\sqrt {-11}}{2}}\right)$	$\mathbb {Z} [{\sqrt {11}}]$	$(-1)(3\pm {\sqrt {11}})3^{2}(4\pm {\sqrt {11}})$
$\mathbb {Z} [{\sqrt {-13}}]$	2 × 3 2 × 5	${\mathcal {O}}_{\mathbb {Q} ({\sqrt {13}})}$	$(-1)2\left({\frac {1}{2}}\pm {\frac {\sqrt {13}}{2}}\right)^{2}5$
$\mathbb {Z} [{\sqrt {-14}}]$		$\mathbb {Z} [{\sqrt {14}}]$	$(-1)(4\pm {\sqrt {14}})3^{2}(3\pm {\sqrt {14}})$
${\mathcal {O}}_{\mathbb {Q} ({\sqrt {-15}})}$		$\mathbb {Z} [{\sqrt {15}}]$	2 × 3 2 × 5
$\mathbb {Z} [{\sqrt {-17}}]$		${\mathcal {O}}_{\mathbb {Q} ({\sqrt {17}})}$	$(-1)\left({\frac {3}{2}}\pm {\frac {\sqrt {17}}{2}}\right)3^{2}\times 5$
${\mathcal {O}}_{\mathbb {Q} ({\sqrt {-19}})}$	$2\times 3^{2}\left({\frac {1}{2}}-{\frac {\sqrt {-19}}{2}}\right)\left({\frac {1}{2}}+{\frac {\sqrt {-19}}{2}}\right)$	$\mathbb {Z} [{\sqrt {19}}]$	$(-1)(13\pm 3{\sqrt {19}})(4\pm {\sqrt {19}})^{2}(9\pm 2{\sqrt {19}})$