# 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 143

- The largest amount of money one can have in n $1, $2, $5, $10, $20, and $50 bills and not be able to make exact change for a $100 bill
- 143 is the smallest integers n such that the prime factorization of n uses the proper subset of distinct digits of n (143 = 11
^{1} 13^{1})
- 143 is the smallest Tnaillirb: a brilliant number whose reversal is a different brilliant number. This is a special subset of emirpimes, with only 102 examples below 100000
- 143 is the smallest number n such that the last n digits of n
^{n} form a prime number

## Rare Properties of 143

The number n is called an *aspiring* number if its aliquot sequence terminates in a perfect number, and it is not a perfect number itself.

## Common Properties of 143

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 *odd* if it is not divisible by 2.

Numbers that are not odd are even. 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.