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

1,8

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.

Links

Table of n, a(n) for n=1..90.

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

Example

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

Mathematica

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

Prog

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

Crossrefs

Inspired by A291900.

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

Sequence in context: A160812 A338271 A176866 * A347403 A063918 A271419

Adjacent sequences: A294611 A294612 A294613 * A294615 A294616 A294617

Keyword

nonn,easy

Author

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

Status

approved