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# 45

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

REMARKS

TABLE

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]

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).

 ${\displaystyle -1}$ 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