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45

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This article is under construction.            

Please do not rely on any information it contains.            


45 is an integer.

Membership in core sequences

Odd numbers ..., 39, 41, 43, 45, 47, 49, 51, ... A005408
Composite numbers ..., 40, 42, 44, 45, 46, 48, 49, ... A002808
Triangular numbers ..., 21, 28, 36, 45, 55, 66, 78, ... A000217
Little Schroeder numbers 1, 1, 3, 11, 45, 197, 903, 4279, ... A001003
Numbers that are the sum of two squares ..., 37, 40, 41, 45, 49, 50, 52, ... A001481

Like all triangular numbers, 45 occurs more than twice in Pascal's triangle, specifically, 45 occurs four times.

Sequences pertaining to 45

Multiples of 45 0, 45, 90, 135, 180, 225, 270, 315, 360, 405, ...

Partitions of 45

There are 89134 partitions of 45.

The Goldbach representations of 45 using distinct primes are: 43 + 2 = 37 + 5 + 3 = 31 + 11 + 3 = 29 + 13 + 3 = 29 + 11 + 5 = 23 + 19 + 3 = 23 + 17 + 5 = 45.

Roots and powers of 45

In the table below, irrational numbers are given truncated to eight decimal places.

TABLE GOES HERE

Logarithms and 45th powers

REMARKS

TABLE

Values for number theoretic functions with 45 as an argument

TABLE GOES HERE

Factorization of some small integers in a quadratic integer ring adjoining the square roots of −45, 45

Since 45 is not squarefree, [FINISH WRITING]

Factorization of 45 in some quadratic integer rings

PLACEHOLDER

TABLE GOES HERE

Representation of 45 in various bases

Base 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
Representation 101101 1200 231 140 113 63 55 50 45 41 39 36 33 30 2D 2B 29 27 25

The square of 45 is 2025. Notice that 20 + 25 = 45. This means that 45 is a base 10 Kaprekar number (see A006886).

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