36

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36 is an integer. As the square of 6, it is the smallest nontrivial square to also be a triangular number.

Membership in core sequences

Even numbers	..., 30, 32, 34, 36, 38, 40, 42, ...	A005843
Composite numbers	..., 33, 34, 35, 36, 38, 39, 40, ...	A002808
Abundant numbers	12, 18, 20, 24, 30, 36, 40, 42, ...	A005101
Triangular numbers	..., 15, 21, 28, 36, 45, 55, 66, ...	A000217
Perfect squares	1, 4, 9, 16, 25, 36, 49, 64, 81, ...	A000290
Loeschian numbers	..., 27, 28, 31, 36, 37, 39, 43, ...	A003136

Sequences pertaining to 36

Multiples of 36	0, 36, 72, 108, 144, 180, 216, 252, 288, 324, 360, 396, 432, ...	A044102
Divisors of 36	1, 2, 3, 4, 6, 9, 12, 18, 36	A018256

Partitions of 36

There are 17977 partitions of 36.

The Goldbach representations of 36 are 5 + 31 = 7 + 29 = 13 + 23 = 17 + 19.

Roots and powers of 36

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

${\sqrt {36}}$	6.00000000		36 2	1296
${\sqrt[{3}]{36}}$	3.30192724	A010607	36 3	46656
${\sqrt[{4}]{36}}$	2.44948974	A010464	36 4	1679616
${\sqrt[{5}]{36}}$	2.04767251	A011121	36 5	60466176
${\sqrt[{6}]{36}}$	1.81712059	A005486	36 6	16777216
${\sqrt[{7}]{36}}$	1.66851044		36 7	78364164096
${\sqrt[{8}]{36}}$	1.56508458	A011004	36 8	2821109907456
${\sqrt[{9}]{36}}$	1.48909532		36 9	101559956668416
${\sqrt[{10}]{36}}$	1.43096908	A011091	36 10	3656158440062976
${\sqrt[{11}]{36}}$	1.38510292		36 11	131621703842267136
${\sqrt[{12}]{36}}$	1.34800615	A011215	36 12	4738381338321616896
				A009980

Logarithms and 36th 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.

From Fermat's little theorem it follows that if $b$ is coprime to 37, then $b^{36}\equiv 1\mod 37$.

If $n$ is not a multiple of 73, then either $n^{36}-1$ or $n^{36}+1$ is. Hence the formula for the Legendre symbol $\left({\frac {a}{73}}\right)=a^{36}\mod 73$.

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

TABLE GOES HERE

Values for number theoretic functions with 36 as an argument

$\mu (36)$	0
$M(36)$	−1
$\pi (36)$	11
$\sigma _{1}(36)$
$\sigma _{0}(36)$
$\phi (36)$	12
$\Omega (36)$	4
$\omega (36)$	2
$\lambda (36)$		This is the Carmichael lambda function.
$\lambda (36)$		This is the Liouville lambda function.
36!	371993326789901217467999448150835200000000
$\Gamma (36)$	10333147966386144929666651337523200000000

Factorization of 36 in some quadratic integer rings

TABLE GOES HERE

Representation of 36 in various bases

Base	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18	19	20
Representation	100100	1100	210	121	100	51	44	40	36	33	30	2A	28	26	24	22	20	1H	1G

In theory, any integer greater than 1 can be used as a base for a positional numeral system. In practice, however, the large number of symbols required keeps bases beyond sexagesimal firmly in the realm of theory.

If we use letters of the Latin alphabet to represent digits above 9, then we have A = 9 + 1, B = 9 + 2, C = 9 + 3, and so on and so forth to Z = 9 + 26. For this scheme, then base 36 is the largest base that can be used. It is possible to extend this to go further, of course, such as by distinguishing between uppercase and lowercase letters (e.g., A could correspond to 10, a could correspond to 36).

36 is a Harshad number in bases 2 through 13, except for base 7.

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