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125
125 is an integer. It is the only number with a base 10 representation that contains the base 10 representations of its divisors (1, 5, 25) as proper substrings.
Contents
- 1 Membership in core sequences
- 2 Sequences pertaining to 125
- 3 Partitions of 125
- 4 Roots and powers of 125
- 5 Logarithms and 125th powers
- 6 Values for number theoretic functions with 125 as an argument
- 7 Factorization of 125 in some quadratic integer rings
- 8 Representation of 125 in various bases
- 9 See also
- 10 References
Membership in core sequences
Odd numbers | ..., 119, 125, 123, 125, 127, 129, 131, ... | A005408 |
Composite numbers | ..., 122, 123, 124, 125, 126, 128, 129, ... | A002808 |
Perfect cubes | ..., 8, 27, 64, 125, 216, 343, 512, ... | A000578 |
Number of trees on labeled nodes | 1, 1, 1, 3, 16, 125, 1296, 16807, 262144, ... | A000124 |
Numbers that are the sum of 2 squares | ..., 117, 121, 122, 125, 128, 130, 136, ... | A001481 |
Sequences pertaining to 125
Multiples of 125 | 125, 250, 375, 500, 625, 750, 875, 1000, 1125, 1250, ... | |
sequence starting at 97 | ..., 83, 250, 125, 376, 188, 94, 47, 142, 71, 214, ... | A008873 |
Partitions of 125
There are 3163127352 partitions of 125.
Since 123 is composite, any prime partition of 125 must consist of at least three parts.
Roots and powers of 125
In the table below, irrational numbers are given truncated to eight decimal places.
TABLE GOES HERE
Logarithms and 125th powers
In the OEIS specifically and mathematics in general, refers to the natural logarithm of , 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 125 as an argument
TABLE GOES HERE
Factorization of 125 in some quadratic integer rings
As was mentioned above, 125 is the cube of 5. But it has different factorizations in some quadratic integer rings, and in a few cases it's not a simple matter of taking the factorization of 5 and adding in some exponent 3s.
5 3 5 3 5 3 5 3 5 3 5 3 5 3
Representation of 125 in various bases
Base | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 |
Representation | 1111101 | 11122 | 1331 | 1000 | 325 | 236 | 175 | 148 | 125 | 104 | A5 | 98 | 8D | 85 | 7D | 76 | 6G | 6B | 65 |
In decimal, 125 is a Friedman number, since .
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 |