A284443 a(n) = Sum_{d|n, d == 2 (mod 7)} d.

0, 2, 0, 2, 0, 2, 0, 2, 9, 2, 0, 2, 0, 2, 0, 18, 0, 11, 0, 2, 0, 2, 23, 2, 0, 2, 9, 2, 0, 32, 0, 18, 0, 2, 0, 11, 37, 2, 0, 2, 0, 2, 0, 46, 9, 25, 0, 18, 0, 2, 51, 2, 0, 11, 0, 2, 0, 60, 0, 32, 0, 2, 9, 18, 65, 2, 0, 2, 23, 2, 0, 83, 0, 39, 0, 2, 0, 2, 79, 18, 9

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. A109704.

Cf. Sum_{d|n, d == k (mod 7)} d: A284099 (k=1), this sequence (k=2), A284444 (k=3), A284445 (k=4), A284446 (k=5), A284105 (k=6).

Programs

Mathematica

Table[Sum[If[Mod[d, 7] == 2, d, 0], {d, Divisors[n]}], {n, 80}] (* Indranil Ghosh, Mar 27 2017 *)

PARI

a(n) = sumdiv(n, d, d*((d % 7) == 2)); \\ Amiram Eldar, Nov 26 2023

Formula

G.f.: Sum_{k>=0} (7*k + 2)*x^(7*k+2)/(1 - x^(7*k+2)). - 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