Number Theory
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Sum of Divisors

Sum of all divisors from prime factorization.

Formula

σ(n)=∏piai+1−1pi−1\sigma(n) = \prod \frac{p_i^{a_i+1}-1}{p_i - 1}

Variables

p_iPrimes
a_iExponents

Example

Related to perfect numbers

Did You Know?

The sum-of-divisors function unlocks the ancient mystery of perfect and amicable numbers.

divisors