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 392
- 392 is the smallest Achilles number which is coprime to the sum of its divisors (Achilles numbers are powerful but not perfect powers)
Common Properties of 392
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.
An integer n is powerful if for every prime p dividing n, p2 also divides n.
How much power? They all can be written as a2 b3.
The number n is practical if all numbers strictly less than n are sums of distinct divisors of n.