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140
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140 is an integer, and a harmonic divisor number (see A001599), the second one not to be an even perfect number.
Contents
- 1 Membership in core sequences
- 2 Sequences pertaining to 140
- 3 Partitions of 140
- 4 Roots and powers of 140
- 5 Values for number theoretic functions with 140 as an argument
- 6 Factorization of some small integers in a quadratic integer ring adjoining −140, 140
- 7 Factorization of 140 in some quadratic integer rings
- 8 Representation of 140 in various bases
- 9 See also
Membership in core sequences
Even numbers | ..., 134, 136, 138, 140, 142, 144, 146, ... | A005843 |
Composite numbers | ..., 135, 136, 138, 140, 141, 142, 143, ... | A002808 |
Abundant numbers | ..., 126, 132, 138, 140, 144, 150, 156, ... | A005101 |
Square pyramidal numbers | ..., 30, 55, 91, 140, 204, 285, 385, 506, ... | A000330 |
Sequences pertaining to 140
Divisors of 140 | 1, 2, 4, 5, 7, 10, 14, 20, 28, 35, 70, 140 | A018301 |
Multiples of 140 | 0, 140, 280, 420, 560, 700, 840, 980, 1120, 1260, 1400, 1540, ... | |
sequence beginning at 63 | 63, 188, 94, 47, 140, 70, 35, 104, 52, 26, 13, 38, 19, 56, 28, ... | A008895 |
Note that 140 has twelve divisors which add up to 336. The harmonic mean is therefore , and since that's an integer, 140 is a harmonic divisor number (A001599).
Partitions of 140
There are 15065878135 partitions of 140.
The Goldbach representations of 140 are: 137 + 3 = 127 + 13 = 109 + 31 = 103 + 37 = 97 + 43 = 79 + 61 = 73 + 67 = 140.
Roots and powers of 140
In the table below, irrational numbers are given truncated to eight decimal places.
PLACEHOLDER
Values for number theoretic functions with 140 as an argument
PLACEHOLDER
Factorization of some small integers in a quadratic integer ring adjoining −140, 140
PLACEHOLDER
Factorization of 140 in some quadratic integer rings
PLACEHOLDER
TABLE GOES HERE
Representation of 140 in various bases
Base | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 |
Representation | 10001100 | 12012 | 2030 | 1030 | 352 | 260 | 214 | 165 | 140 | 118 | B8 | AA | A0 | 95 | 8C | 84 | 7E | 77 | 70 |
140 is a Harshad number in bases 4, 5, 6, 8, 10, 11, 13, 14, 15, 16, 19, 20, etc.
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 |