A294614 Sum of the divisors of 12*n - 1, divided by 12, minus n.

0, 0, 1, 0, 0, 0, 0, 2, 0, 2, 0, 2, 3, 0, 0, 0, 3, 4, 0, 0, 0, 0, 8, 4, 3, 0, 3, 6, 0, 0, 5, 0, 7, 4, 0, 0, 0, 18, 0, 0, 0, 0, 9, 4, 12, 4, 0, 14, 0, 0, 5, 8, 11, 0, 0, 6, 0, 12, 9, 0, 5, 0, 13, 6, 5, 10, 7, 14, 0, 0, 5, 0, 31, 0, 5, 0, 7, 30, 0, 12, 0, 0, 17, 6, 0, 0, 13, 18, 9, 8

Offset: 1

Author

Omar E. Pol and Robert G. Wilson v, Nov 04 2017

Keywords

• nonn
• easy

Comments

a(n) = 0 iff n is in A138620.

First occurrence of k > -1: 1, 3, 8, 13, 18, 31, 28, 33, 23, 43, 66, 53, 45, 63, 48, 101, 166, etc.

Examples

			a(13) = 3 since d(12*13-1)/12 - 13 = 192/12 - 13 = 16 - 13 = 3.
		

Crossrefs

Inspired by A291900.

Cf. A000203, A017653, A068231, A086463, A138620.

Programs

Mathematica

a[n_] := DivisorSigma[1, 12 n - 1]/12 - n; Array[a, 90]

PARI

a(n) = sigma(12*n-1)/12 - n;

Formula

a(n) = sigma(12*n-1)/12 - n = A000203(A017653(n-1))/12 - n.

Sum_{k=1..n} a(k) = c * n^2 + O(n*log(n)), where c = Pi^2/18 - 1/2 = 0.048311... . - Amiram Eldar, Mar 28 2024