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 45
- 45 is the only number that is the sum of its digits multiplied by 5
- 45 is the smallest deficient number that is not distended, where distended numbers are positive integers n for which each divisor of n is greater than the sum of all smaller divisors
- 45 is the smallest composite super-Catalan number
- 45 can be partitioned into two parts that concatenate to its square: 45 = 20 + 25 and 452 = 2025. Also, 45 can be partitioned into three parts that concatenate to its cube: 45 = 9 + 11 + 25 and 453 = 91125. Moreover, 45 can be partitioned into four parts that concatenate to its fourth power: 45 = 4 + 10 + 06 + 25 and 454 = 4100625
Common Properties of 45
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.