A284445 a(n) = Sum_{d|n, d == 4 (mod 7)} d.

0, 0, 0, 4, 0, 0, 0, 4, 0, 0, 11, 4, 0, 0, 0, 4, 0, 18, 0, 4, 0, 11, 0, 4, 25, 0, 0, 4, 0, 0, 0, 36, 11, 0, 0, 22, 0, 0, 39, 4, 0, 0, 0, 15, 0, 46, 0, 4, 0, 25, 0, 4, 53, 18, 11, 4, 0, 0, 0, 64, 0, 0, 0, 36, 0, 11, 67, 4, 0, 0, 0, 22, 0, 74, 25, 4, 11, 39, 0, 4, 81

Offset: 1

Author

Seiichi Manyama, Mar 27 2017

Keywords

• nonn
• easy

Links

• Seiichi Manyama, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A109706.

Cf. Sum_{d|n, d == k (mod 7)} d: A284099 (k=1), A284443 (k=2), A284444 (k=3), this sequence (k=4), A284446 (k=5), A284105 (k=6).

Programs

Mathematica

Table[Sum[If[Mod[d, 7] == 4, d, 0], {d, Divisors[n]}], {n, 80}] (* Indranil Ghosh, Mar 27 2017 *)

PARI

a(n) = sumdiv(n, d, d*((d % 7) == 4)); \\ Amiram Eldar, Nov 26 2023

Formula

G.f.: Sum_{k>=0} (7*k + 4)*x^(7*k+4)/(1 - x^(7*k+4)). - Ilya Gutkovskiy, Mar 28 2017

Sum_{k=1..n} a(k) = c * n^2 + O(n*log(n)), where c = Pi^2/84 = 0.117495... . - Amiram Eldar, Nov 26 2023