A284444 a(n) = Sum_{d|n, d == 3 (mod 7)} d.

0, 0, 3, 0, 0, 3, 0, 0, 3, 10, 0, 3, 0, 0, 3, 0, 17, 3, 0, 10, 3, 0, 0, 27, 0, 0, 3, 0, 0, 13, 31, 0, 3, 17, 0, 3, 0, 38, 3, 10, 0, 3, 0, 0, 48, 0, 0, 27, 0, 10, 20, 52, 0, 3, 0, 0, 3, 0, 59, 13, 0, 31, 3, 0, 0, 69, 0, 17, 3, 10, 0, 27, 73, 0, 3, 38, 0, 3, 0, 90, 3

Offset

1,3

Links

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

Formula

G.f.: Sum_{k>=0} (7*k + 3)*x^(7*k+3)/(1 - x^(7*k+3)). - 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

Mathematica

Table[Sum[If[Mod[d, 7] == 3, d, 0], {d, Divisors[n]}], {n, 80}] (* Indranil Ghosh, Mar 27 2017 *)

Prog

(PARI) a(n) = sumdiv(n, d, d*((d % 7) == 3)); \\ Amiram Eldar, Nov 26 2023

Crossrefs

Cf. A109705.

Cf. Sum_{d|n, d == k (mod 7)} d: A284099 (k=1), A284443 (k=2), this sequence (k=3), A284445 (k=4), A284446 (k=5), A284105 (k=6).

Sequence in context: A021337 A361824 A293903 * A341794 A033685 A272974

Adjacent sequences: A284441 A284442 A284443 * A284445 A284446 A284447

Keyword

nonn,easy

Author

Seiichi Manyama, Mar 27 2017

Status

approved