The odd divisor function σ_k^(o)(n) = sum_(d|n d odd) d^k is the sum of kth powers of the odd divisors of a number n. It is the analog of the divisor function for odd divisors only. For the case k = 1, σ_1^(o)(n) | = | sum_(d|n d odd) d | = | sum_(d|n) ((-1)^(d + 1) n)/d | = | σ_1(n) - 2σ_1(n/2), where σ_k(n/2) is defined to be 0 if n is odd.

divisor function | even divisor function