# 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 190

- 190 is the largest number with only distinct prime Roman numeral palindrome factors that is itself a Roman numeral palindrome (190 = CXC = II * V * XIX)
- 190 is the smallest non-palindrome that shares the number of totatives with its reversal
- 190 is the smallest anagrasum integer: its set of digits is the same as the set of digits that is formed by sums of pairs of its adjacent digits
- 190 is the smallest multiple of 10 such that its digit sum is also a multiple of 10

## Common Properties of 190

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.

One can take the sum of the squares of the digits of a number. Those numbers are *happy* for which iterating this operation eventually leads to 1.

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

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.