Question

if $a$ is the sum of the positive divisors of $500$, what is the sum of the distinct prime divisors of $a$?

Answer 1

25

Explanation:

You want the sum of the distinct prime divisors of the sum of the positive divisors of 500.

Divisors of 500

The prime factorization of 500 is ...

500 = 2²·5³

so there are (2+1)(3+10 = 12 positive integer divisors:

1, 2, 4, 5, 10, 20, 25, 50, 100, 125, 250, 500

The sum of these divisors is 1092.

Divisors of 1092

The prime factorization of 1092 is ...

1092 = 2²·3·7·13

so the sum of interest is ...

2 +3 +7 +13 = 25

The sum of interest is 25.