The number 153

The number 153 has very peculiar properties :

It is the smallest number that can be expressed as the sum of the cubes of its digits :

153 = 13 + 53 + 33

It is equal to the sum of the factorials of the numbers from 1 to 5 :

153 = 1! + 2! + 3 ! + 4! +5 !

The sum of its digits is a perfect square :

1 + 5 + 3 = 9 = 32

The sum of its divisors (excluding the number itself ) is also a perfect square :

1 + 3 + 9 + 17 + 51 = 81 = 92

Moreover, as can be seen , is the square of the sum of the digits.

Can be expressed as the sum of all integers from 1 to 17 :

153 = 1 + 2 + 3 + 4 + ... + 15 + 16 + 17

This means that 153 is the seventeenth triangular number .

Is divisible by the sum of its digits :

153 / (1 + 5 + 3) = 17

Can be expressed as the product of two numbers formed by the digits :

153 = 3 · 51

It can also be expressed in this curious way :

135 = 11 + 32 + 53

The sums of powers 0, 1 and 2 of its digits is equal to the product of them :

10 + 51 + 32 = 1 · 5 · 3