# Number Gossip

(Enter a number and I'll tell you everything you wanted to know about it but were afraid to ask.)

## Unique Properties of 153

- 153 is the smallest number (except 1) such that its sum of the cubes of the digits equals itself: 153 = 1
^{3} + 5^{3} + 3^{3}
- 153 is the smallest non-palindromic triangular number whose reverse is a triangular number with the same number of digits
- 153 = 1! + 2! + 3! + 4! + 5!

## Rare Properties of 153

A k-digit number n is called *narcissistic* if it is equal to the sum of k-th powers of its digits. They are also called *Plus Perfect* numbers.

The number n is called a *vampire* number if there exists a factorization of n using n's digits (counting multiplicity).

## Common Properties of 153

A positive integer greater than 1 that is not prime is called *composite*.

Composite numbers are opposite to prime numbers.

The number n is *deficient* if the sum of all its positive divisors except itself is less than n.

Compare with perfect and abundant numbers.

The number n is *evil* if it has an even number of 1's in its binary expansion.

Guess what odious numbers are.

A number is *odd* if it is not divisible by 2.

Numbers that are not odd are even. Compare with another pair -- evil and odious numbers.

If you start with n points on a line, then draw n-1 points above and between, then n-2 above and between them, and so on, you will get a triangle of points. The number of points in this triangle is a *triangle* number.

Compare to square, pentagonal and tetrahedral numbers.