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144
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144 is an integer, the square of 12.
Contents
Membership in core sequences
Even numbers | ..., 138, 140, 142, 144, 146, 148, 150, ... | A005843 |
Composite numbers | ..., 8, 9, 10, 144, 145, 146, 147, 148, ... | A002808 |
Abundant numbers | ..., 132, 138, 140, 144, 150, 156, 160, ... | A005101 |
Fibonacci numbers | ..., 34, 55, 89, 144, 233, 377, 610, ... | A000045 |
Perfect squares | ..., 81, 100, 121, 144, 169, 196, 225, ... | A000290 |
Loeschian numbers | ..., 129, 133, 139, 144, 147, 148, 151, ... | A003136 |
Note that 144 is both a perfect square and a Fibonacci number. In fact, 144 is the largest perfect power to also be a Fibonacci number (see A227875).
Sequences pertaining to 144
Divisors of 144 | 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144 | A018302 |
Multiples of 144 | 12, 24, 36, 48, 60, 72, 84, 96, 108, 120, 132, 144, ... | A008594 |
Partitions of 144
There are 22540654445 partitions of 144.
The Goldbach representations of 144 are 139 + 5 = 137 + 7 = 131 + 13 = 127 + 17 = 113 + 31 = 107 + 37 = 103 + 41 = 101 + 43 = 97 + 47 = 83 + 61 = 73 + 71 = 144.
Roots and powers of 144
In the table below, irrational numbers are given truncated to eight decimal places.
12.00000000 | A130706 | 144 2 | 20736 | |
5.24148278 | 144 3 | 2985984 | ||
3.46410161 | A010469 | 144 4 | 429981696 | |
2.70192007 | 144 5 | 61917364224 | ||
2.28942848 | A010584 | 144 6 | 8916100448256 | |
2.03393700 | 144 7 | 1283918464548864 | ||
1.86120971 | A011009 | 144 8 | 184884258895036416 | |
1.73707293 | 144 9 | 26623333280885243904 | ||
1.64375182 | A011097 | 144 10 | 3833759992447475122176 | |
1.57113958 | 144 11 | 552061438912436417593344 | ||
1.51308574 | A011305 | 144 12 | 79496847203390844133441536 |
Values for number theoretic functions with 144 as an argument
0 | ||
−1 | ||
34 | ||
403 | ||
15 | ||
48 | ||
6 | ||
2 | ||
This is the Carmichael lambda function. | ||
This is the Liouville lambda function. |
Factorization of 144 in some quadratic integer rings
As was mentioned above, 144 is the product of 2 4 and 3 2. But it has different factorizations in some quadratic integer rings.
PLACEHOLDER
Representation of 144 in various bases
Base | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 |
Representation | 10010000 | 12100 | 2100 | 1034 | 400 | 264 | 220 | 170 | 144 | 121 | 100 | B1 | A4 | 99 | 90 | 88 | 80 | 7B | 74 |
144 is a Harshad number in every base from 2 through 19 except base 14.
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 |