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 = 111 131)
- 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 nn 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.