# 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 77

- 77 is the smallest number with multiplicative persistence 4
- 77 is the largest number that cannot be written as a sum of distinct numbers whose reciprocals sum to 1
- 77 is the smallest number n such that the smallest possible number of multiplications required to compute x to the n-th power is by 1 fewer than the number of multiplications obtained by Knuth's power tree method

## Common Properties of 77

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.

A *palindrome* is a number that reads the same forward or backward.

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.