27

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27 is a composite number, the cube of 3. Its own cube is 19683. Notice that 1 + 9 + 6 + 8 + 3 = 27; no larger number has this property in base 10.

Membership in core sequences

Odd numbers	..., 21, 23, 25, 27, 29, 31, 33, ...	A005408
Composite numbers	..., 24, 25, 26, 27, 28, 30, 32, ...	A002808
Perfect cubes	1, 8, 27, 64, 125, 216, 343, 512, ...	A000578
Powers of 3	1, 3, 9, 27, 81, 243, 729, 2187, ...	A000244
Deficient numbers	..., 23, 25, 26, 27, 29, 31, 32, ...	A005100

In Pascal's triangle, 27 occurs twice.

Sequences pertaining to 27

Multiples of 27	0, 27, 54, 81, 108, 135, 162, 189, 216, 243, 270, 297, 324, ...
27-gonal numbers	1, 27, 78, 154, 255, 381, 532, 708, 909, 1135, 1386, 1662, ...	A255186
Decimal expansion of reciprocal of 27	0.037037037037037037037037037037037037037037037...	A021031
$3x+1$ sequence beginning at 27	27, 82, 41, 124, 62, 31, 94, 47, 142, 71, 214, ... (takes more than a hundred iterations to get to a power of 2)	A008884
$3x-1$ sequence beginning at 27	27, 80, 40, 20, 10, 5, 14, 7, 20, 10, 5, 14, 7, ...

Partitions of 27

There are 3010 partitions of 27.

There are only two partitions of 27 into squares: 2(1 2) + 5 2 and 3(3 2).

The Goldbach representations of 27 using distinct primes are: 3 + 5 + 19 = 3 + 7 + 17 = 3 + 11 + 13 = 27.

Roots and powers of 27

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

${\sqrt {27}}$	5.19615242	A010482	27 2	729
${\sqrt[{3}]{27}}$	3.00000000		27 3	19683
${\sqrt[{4}]{27}}$	2.27950705	A011022	27 4	531441
${\sqrt[{5}]{27}}$	1.93318204	A011112	27 5	14348907
${\sqrt[{6}]{27}}$	1.73205080	A002194	27 6	387420489
${\sqrt[{7}]{27}}$	1.60132888		27 7	10460353203
${\sqrt[{8}]{27}}$	1.50980364		27 8	282429536481
${\sqrt[{9}]{27}}$	1.44224957	A002581	27 9	7625597484987
${\sqrt[{10}]{27}}$	1.39038917		27 10	205891132094649
				A009971

Logarithms and twenty-seventh powers

In the OEIS specifically and mathematics in general, $\log x$ refers to the natural logarithm of $x$, whereas all other bases are specified with a subscript.

As above, irrational numbers in the following table are truncated to eight decimal places.

TABLE GOES HERE

Values for number theoretic functions with 27 as an argument

$\mu (27)$	0
$M(27)$	–1
$\pi (27)$	9
$\sigma _{1}(27)$	40
$\sigma _{0}(27)$	4
$\phi (27)$	18
$\Omega (27)$	3
$\omega (27)$	1
$\lambda (27)$	18	This is the Carmichael lambda function.
$\lambda (27)$	–1	This is the Liouville lambda function.
$\zeta (27)$	1.0000000074507117898...
27!	10888869450418352160768000000
$\Gamma (27)$	403291461126605635584000000

Factorization of some small integers in a quadratic integer ring adjoining the square roots of –27, 27

Since ${\sqrt {27}}=3{\sqrt {3}}$, $\mathbb {Z} [{\sqrt {27}}]$ is a subdomain of $\mathbb {Z} [{\sqrt {3}}]$. A similar situation holds for $\mathbb {Z} [{\sqrt {-27}}]$, but $\mathbb {Z} [{\sqrt {-3}}]$ is not integrally closed either, and it is in fact a subdomain of $\mathbb {Z} [\omega ]$, where $\omega$ is a complex cubic root of 1.

Factorization of 27 in some quadratic integer rings

As was mentioned above, 27 is the cube of 3. But to obtain its factorization in quadratic integer rings, it's not always a matter of taking the factorization of 3 and adding exponent 3s as needed.

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

Representation of 27 in various bases

Base	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18	19	20
Representation	11011	1000	123	102	43	36	33	30	27	25	23	21	1D	1C	1B	1A	19	18	17

Note that 27 is a Harshad number in bases 3, 5, 7, 9, and, breaking the pattern of odd bases, 10. Then bases 13 and 19.

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