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# 140

Please do not rely on any information it contains.

140 is an integer, and a harmonic divisor number (see A001599), the second one not to be an even perfect number.

## 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, ... ${\displaystyle 3x-1}$ 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 ${\displaystyle {\frac {140\times 12}{336}}=5}$, 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

PLACEHOLDER

PLACEHOLDER

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.

 ${\displaystyle -1}$ 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