Divisor Sum of Four-Divisor Numbers

Medium

You are given an array of positive integers numbers. Pick out the ones that have exactly four divisors (counting 1 and the number itself) and add up all the divisors of all those numbers. A number that appears several times is counted every time. If no number qualifies, return 0.

Example 1

numbers=[15, 9, 8] → 39

15 has divisors 1, 3, 5, 15: exactly four, summing to 24. 8 has 1, 2, 4, 8: also four, summing to 15. 9 has only three (1, 3, 9) and does not count. The total is 24 + 15 = 39.

Example 2

numbers=[10, 10, 1] → 36

Each 10 contributes 1 + 2 + 5 + 10 = 18, and repeats count separately: 36. The number 1 has a single divisor.

Example 3

numbers=[2, 4, 16] → 0

None of them has exactly four divisors: 2 has two, 4 has three, 16 has five.

Constraints

1 ≤ len(numbers) ≤ 10⁴
1 ≤ numbers[i] ≤ 10⁵

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Topics

Array Math

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Input

numbers=[15, 9, 8]

Expected

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