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40
From OeisWiki
40 is an integer. In English, it is the only integer with its letters in alphabetical order (f, o, r, t, y).
Contents
- 1 Membership in core sequences
- 2 Sequences pertaining to 40
- 3 Partitions of 40
- 4 Roots and powers of 40
- 5 Logarithms and fortieth powers
- 6 Values for number theoretic functions with 40 as an argument
- 7 Factorization of some small integers in a quadratic integer ring adjoining the square roots of −40, 40
- 8 Factorization of 40 in some quadratic integer rings
- 9 Representation of 40 in various bases
- 10 See also
Membership in core sequences
Even numbers | ..., 34, 36, 38, 40, 42, 44, 46, ... | A005843(20) |
Composite numbers | ..., 36, 38, 39, 40, 42, 44, 45, ... | A002808 |
Abundant numbers | ..., 24, 30, 36, 40, 42, 48, 54, ... | A005101 |
Numbers that are the sum of two squares | ..., 34, 36, 37, 40, 41, 45, 49, ... | A001481 |
Sequences pertaining to 40
Divisors of 40 | 1, 2, 4, 5, 8, 10, 20, 40 | A018257 |
Multiples of 40 | 0, 40, 80, 120, 160, 200, 240, 280, 320, 360, ... | |
Powers of 40 | 1, 40, 1600, 64000, 2560000, 102400000, ... | A009984 |
sequence beginning at 39 | ..., 52, 26, 13, 40, 20, 10, 5, 16, 8, 4, 2, 1, ... | A008878 |
Partitions of 40
There are 37338 partitions of 40.
The Goldbach representations of 40 are: 3 + 37 = 11 + 29 = 17 + 23.
Roots and powers of 40
In the table below, irrational numbers are given truncated to eight decimal places.
6.32455532 | A010494 | 40 2 | 1600 | |
3.41995189 | A010611 | 40 3 | 64000 | |
2.51486685 | A011034 | 40 4 | 2560000 | |
2.09127910 | A011125 | 40 5 | 102400000 | |
1.84931119 | 40 6 | 4096000000 | ||
1.69381398 | 40 7 | 163840000000 | ||
1.58583317 | 40 8 | 6553600000000 | ||
1.50663019 | 40 9 | 262144000000000 | ||
1.44612554 | 40 10 | 10485760000000000 | ||
1.39843349 | 40 11 | 419430400000000000 | ||
1.35989381 | 40 12 | 16777216000000000000 | ||
A009984 |
Logarithms and fortieth powers
PLACEHOLDER
Values for number theoretic functions with 40 as an argument
PLACEHOLDER
Factorization of some small integers in a quadratic integer ring adjoining the square roots of −40, 40
Given that 40 is not squarefree, [FINISH WRITING]
Factorization of 40 in some quadratic integer rings
In , 20 has the prime factorization of 2 2 × 5. But it has different factorizations in some quadratic integer rings.
2 2 × 5 | 2 2 × 5 | ||
2 2 × 5 | |||
2 2 × 5 OR | 2 2 × 5 OR | ||
2 2 × 5 | |||
2 2 × 5 | |||
2 2 × 5 OR | |||
Representation of 40 in various bases
Base | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 |
Representation | 101000 | 1111 | 220 | 130 | 104 | 55 | 50 | 44 | 40 | 37 | 34 | 31 | 2C | 2A | 28 | 26 | 24 | 22 | 20 |
40 is a Harshad number in every base from binary to vigesimal except for duodecimal, bases 14, 15 and 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 |