# 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 276

- 276 is the smallest number whose aliquot sequence is not completely known
- 276 is the smallest integer area of a Robbins pentagon: a cyclic pentagon with integer sides and integer area
- 276 is the sum of the first 3 fifth powers
- 276 is the smallest hexagonal number which is a sum of two other non-zero hexagonal numbers

## Common Properties of 276

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

They are abundant above perfection, not to mention deficiency. See perfect and deficient numbers.

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

Composite numbers are opposite to prime 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 *odious* if it has an odd number of 1's in its binary expansion.

Guess what evil numbers are.

The number n is *practical* if all numbers strictly less than n are sums of distinct divisors of n.

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.

The *untouchable* numbers are those that are not the sum of the proper divisors of any number.