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 70
- 70 is the smallest weird number
- 70 is the largest known number n such that 2n has a digit sum of n (the only other such number known is 5)
- 70 is the only non-trivial square number of cannonballs that can be piled into a square pyramid (submitted by Ken Knowlton)
- 70 is the smallest pentagonal number which is a product of 3 distinct primes (submitted by Massimo Kofler)
- 70 is the smallest number n such that the sum of proper divisors of n exceeds n, yet no subset of them adds to n
Rare Properties of 70
The number n is called a weird number if it is abundant but is not the sum of any subset of its proper factors.
Common Properties of 70
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.
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.
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.