Sum of divisors
Number 6 has divisors 1,2,3,6. Number 6 being of course a divisor of itself, if we exclude this,
numbers 1,2 and 3 are named "proper divisors" of 6 (or "aliquot parts").
Their sum is 1+2+3=6. This number is named a "perfect number", equal to sum of its proper divisors.
- Give the sum of the proper divisors of 600.
- Find all other perfect numbers <100.
- Two numbers such that the sum of aliquot parts of each one equals the other are said to be "amicable".
Find two amicable numbers <1000.
Conversely, we might want to find a number, given the sum of its divisors.
- Find all numbers whose sum of all divisors equals 56.
- sum of divisors