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 153
- 153 is the smallest number (except 1) such that its sum of the cubes of the digits equals itself: 153 = 13 + 53 + 33
- 153 is the smallest non-palindromic triangular number whose reverse is a triangular number with the same number of digits
Rare Properties of 153
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.
The number n is called a vampire number if there exists a factorization of n using n's digits (counting multiplicity).
Common Properties of 153
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.
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.