A178636 If n = Product (p_i^k_i) for i = 1, ..., j then a(n) is the sum of the divisors d that are not in the set {1, p_1^k_1, p_2^k_2, ..., p_j^k_j}.

0, 0, 0, 2, 0, 6, 0, 6, 3, 10, 0, 20, 0, 14, 15, 14, 0, 27, 0, 32, 21, 22, 0, 48, 5, 26, 12, 44, 0, 61, 0, 30, 33, 34, 35, 77, 0, 38, 39, 76, 0, 83, 0, 68, 63, 46, 0, 104, 7, 65, 51, 80, 0, 90, 55, 104, 57, 58, 0, 155, 0, 62, 87, 62, 65, 127, 0, 104, 69, 129, 0, 177, 0, 74, 95, 116, 77, 149, 0, 164, 39, 82, 0, 209, 85, 86, 87, 160, 0, 217, 91, 140, 93, 94, 95, 216, 0, 119, 135, 187

Offset: 1

Author

Jaroslav Krizek, Dec 25 2010

Keywords

• nonn

Examples

			For n = 12, set of divisors {1, p_1^k_1, p_2^k_2, ..., p_j^k_j}: {1, 3, 4}. Complement of divisors: {2, 6, 12}. a(12) = 2+6+12 = 20.
		

Formula

a(n) = A000203(n) - A159077(n) = A167515(n) - 1.

a(1) = 0, a(p) = 0, a(pq) = pq, a(pq...z) = [(p+1)* (q+1)* ... *(z+1)] - [p+q+ ...+z] - 1, a(p^k) = (p^k-p)/(p-1), for p, q = primes, k = natural numbers, pq...z = product of k (k > 2) distinct primes p, q, ..., z.

Extensions

I edited the definition to fix the grammar and make it understandable.

a(100) corrected by Georg Fischer, Dec 10 2022