# 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 136

- 136 is the smallest magical sum of a 3 by 3 semimagic squares composed of triangular numbers and squares
- 136 is the sum of distinct squares 36 and 100 of the smallest two numbers with more than one prime factor
- 136 is the smallest number (except 1) such that the sum of the cubes of the digits of the sum of the cubes of the digits of n equals n: 1
^{3} + 3^{3} + 6^{3} = 244 and 2^{3} + 4^{3} + 4^{3} = 136
- 136 is the smallest number n such that reverse(σ(n)) = n − φ(n) = cototient(n)
- 136 is the smallest number n where n and n-1 are both products of 4 primes

## Common Properties of 136

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.

A number is *even* if it is divisible by 2.

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

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

Guess what odious numbers are.

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.