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37

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This article is under construction.            

Please do not rely on any information it contains.            


37 is is the maximum number of fifth powers needed to sum to any number.

Membership in core sequences

Odd numbers ..., 31, 33, 35, 37, 39, 41, 43, ... A005408
Prime numbers ..., 23, 29, 31, 37, 41, 43, 47, ... A000040
Squarefree numbers ..., 33, 34, 35, 37, 38, 39, 41, ... A005117

In Pascal's triangle, 37 occurs twice.

Sequences pertaining to 37

Multiples of 37 0, 37, 74, 111, 148, 185, 222, 259, 296, 333, 370, 407, 444, ... A085959
sequence starting at 87 87, 262, 131, 394, 197, 592, 296, 148, 74, 37, 112, 56, 28, ... A008879

Partitions of 37

PLACEHOLDER

Roots and powers of 37

PLACEHOLDER

Logarithms and 37th powers

REMARKS

TABLE

Values for number theoretic functions with 37 as an argument

–1
–2
11
38
2
36
1
1
36 This is the Carmichael lambda function.
–1 This is the Liouville lambda function.
37! 13763753091226345046315979581580902400000000
371993326789901217467999448150835200000000

Factorization of some small integers in a quadratic integer ring adjoining ,

The commutative quadratic integer ring with unity , with units of the form (), is a unique factorization domain, and it is norm-Euclidean.

2 Prime
3
4 2 2
5 Prime
6
7
8 2 3
9
10 2 × 5
11
12
13 Prime
14
15
16 2 4
17 Prime
18
19 Prime
20 2 2 × 5

Unlike , is not a unique factorization domain. But the window of 2 through 21 does not provide as interesting a window for the of the [FINISH WRITING]

Factorization of 37 in some quadratic integer rings

PLACEHOLDER

TABLE GOES HERE

Representation of 37 in various bases

Base 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
Representation 100101 1101 211 122 101 52 45 41 37 34 31 2B 29 27 25 23 21 1I 1H

REMARKS GO HERE

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