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18
18 is an integer, the only positive integer that is twice the sum of its base 10 digits (see A169805).
Contents
- 1 Membership in core sequences
- 2 Sequences pertaining to 18
- 3 Partitions of 18
- 4 Roots and powers of 18
- 5 Logarithms and eighteenth powers
- 6 Values for number theoretic functions with 18 as an argument
- 7 Factorization of 18 in some quadratic integer rings
- 8 Representation of 18 in various bases
- 9 See also
Membership in core sequences
Even numbers | ..., 12, 14, 16, 18, 20, 22, 24, ... | A005843 |
Composite numbers | ..., 14, 15, 16, 18, 20, 21, 22, ... | A002808 |
Lucas numbers | 2, 1, 3, 4, 7, 11, 18, 29, 47, 76, ... | A000032 |
Abundant numbers | 12, 18, 20, 24, 30, 36, 40, 42, ... | A005101 |
Numbers that are the sum of two squares | ..., 13, 16, 17, 18, 20, 25, 26, ... | A001481 |
Sequences pertaining to 18
Multiples of 18 | 0, 18, 36, 54, 72, 90, 108, 126, 144, 162, 180, 198, 216, ... | A008600 |
Octadecagonal numbers | 1, 18, 51, 100, 165, 246, 343, 456, 585, 730, 891, 1068, ... | A051870 |
sequence starting at 36 | 36, 18, 9, 26, 13, 38, 19, 56, 28, 14, 7, 20, 10, 5, 14, 7, ... | A008894 |
sequence starting at 11 | 11, 56, 28, 14, 7, 36, 18, 9, 46, 23, 116, 58, 29, 146, 73, ... | A259193 |
Partitions of 18
There are 385 partitions of 18.
The Goldbach representations of 18 are: 13 + 5 = 11 + 7 = 18.
Roots and powers of 18
In the table below, irrational numbers are given truncated to eight decimal places.
4.24264068 | A010474 | 18 2 | 324 | |
2.62074139 | A010590 | 18 3 | 5832 | |
2.05976714 | A011014 | 18 4 | 104976 | |
1.78260245 | A011103 | 18 5 | 1889568 | |
1.61887040 | A011395 | 18 6 | 34012224 | |
1.51120939 | A011396 | 18 7 | 612220032 | |
1.43518888 | A011397 | 18 8 | 11019960576 | |
1.37871570 | A011398 | 18 9 | 198359290368 | |
1.33514136 | A011399 | 18 10 | 3570467226624 | |
1.30051594 | A011400 | 18 11 | 64268410079232 | |
1.27234838 | A011401 | 18 12 | 1156831381426176 | |
A001027 |
Logarithms and eighteenth powers
In the OEIS specifically and mathematics in general, refers to the natural logarithm of , whereas all other bases are specified with a subscript.
If is not a multiple of 37, then either or is. Hence the formula for the Legendre symbol .
As above, irrational numbers in the following table are truncated to eight decimal places.
TABLE GOES HERE
(See A010806 for the eighteenth powers of integers).
Values for number theoretic functions with 18 as an argument
0 | ||
−2 | ||
7 | ||
39 | ||
18 | ||
6 | ||
3 | ||
2 | ||
6 | This is the Carmichael lambda function. | |
−1 | This is the Liouville lambda function. | |
= 1.000003817293... See A013676. | ||
18! | 6402373705728000 | |
355687428096000 |
Factorization of 18 in some quadratic integer rings
As was mentioned above, 18 is composite in . But it has different factorizations in some quadratic integer rings.
2 × 3 2 | 2 × 3 2 | ||
2 × 3 2 | 2 × 3 2 | ||
2 × 3 2 | |||
2 × 3 2 | |||
Representation of 18 in various bases
Base | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 through 36 |
Representation | 10010 | 200 | 102 | 33 | 30 | 24 | 22 | 20 | 18 | 17 | 16 | 15 | 14 | 13 | 12 | 11 | 10 | I |
18 is a Harshad number in every base from binary to decimal except for octal. It is also a Harshad number in base 13, hexadecimal, base 17 and base 18.
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 |