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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.

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

Logarithms and 36th powers

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

From Fermat's little theorem it follows that if is coprime to 37, then .

If is not a multiple of 73, then either or is. Hence the formula for the Legendre symbol .

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

0
−1
11
12
4
2
This is the Carmichael lambda function.
This is the Liouville lambda function.
36! 371993326789901217467999448150835200000000
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
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

References