This site is supported by donations to The OEIS Foundation.

144

From OeisWiki
Jump to: navigation, search


This article is under construction.            

Please do not rely on any information it contains.            


144 is an integer, the square of 12.

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

Some integers
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

References