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 1260
- 1260 is the smallest number n such that φ(n+1) = 4φ(n)
Rare Properties of 1260
The number is called pronic if it is the product of two consecutive numbers.
They are twice triangular 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 1260
The number n is abundant if the sum of all its positive divisors except itself is more than n.
They are abundant above perfection, not to mention deficiency. See perfect and deficient numbers.
A positive integer greater than 1 that is not prime is called composite.
Composite numbers are opposite to prime 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.
The number n is practical if all numbers strictly less than n are sums of distinct divisors of n.