# 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 370

- 370 is the smallest sum of two primes squares that is also a sum of two primes cubes (370 = 3
^{2}+19^{2} = 3^{3}+7^{3})
- 370 is the smallest non-repdigit number that is the average of the numbers formed by all permutations of its digits (370 = (073+037+307+370+703+730)/6)
- 370 is one of four numbers that equals the sum of the cubes of its digits: 370 = 3
^{3} + 7^{3} + 0^{3}

## Rare Properties of 370

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.

## Common Properties of 370

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 *odious* if it has an odd number of 1's in its binary expansion.

Guess what evil numbers are.

A number is said to be *square-free* if its prime decomposition contains no repeated factors.

The next *Ulam* number is uniquely the sum of two earlier distinct Ulam numbers.