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37
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37 is is the maximum number of fifth powers needed to sum to any number.
Contents
- 1 Membership in core sequences
- 2 Sequences pertaining to 37
- 3 Partitions of 37
- 4 Roots and powers of 37
- 5 Logarithms and 37th powers
- 6 Values for number theoretic functions with 37 as an argument
- 7 Factorization of some small integers in a quadratic integer ring adjoining ,
- 8 Factorization of 37 in some quadratic integer rings
- 9 Representation of 37 in various bases
- 10 See also
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
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 |