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 5187
- 5187 is the smallest number n such that φ(n) = (φ(n+1) + φ(n-1))/2
- 5187 is the smallest odd number having exactly three prime gaps in its factorization (5187 = 3*7*13*19) (submitted by Massimo Kofler)
Common Properties of 5187
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.
One can take the sum of the squares of the digits of a number. Those numbers are happy for which iterating this operation eventually leads to 1.
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.