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 315
- 315 is the smallest n such that φ(n-1) + φ(n+1) = σ(n)/2
- 315 is the smallest not squarefree order of a cyclotomic polynomial containing a coefficient with an absolute value greater than one
- 315 is the smallest odd number such that its sum of divisors is larger than the sums of divisors of its neighbors
Common Properties of 315
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.