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 136
- 136 is the smallest magical sum of a 3 by 3 semimagic squares composed of triangular numbers and squares
- 136 is the sum of distinct squares 36 and 100 of the smallest two numbers with more than one prime factor
- 136 is the smallest number (except 1) such that the sum of the cubes of the digits of the sum of the cubes of the digits of n equals n: 13 + 33 + 63 = 244 and 23 + 43 + 43 = 136
- 136 is the smallest number n such that reverse(σ(n)) = n − φ(n) = cototient(n)
- 136 is the smallest number n where n and n-1 are both products of 4 primes
Common Properties of 136
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.
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.