A284104 a(n) = Sum_{d|n, d == 5 (mod 6)} d.

0, 0, 0, 0, 5, 0, 0, 0, 0, 5, 11, 0, 0, 0, 5, 0, 17, 0, 0, 5, 0, 11, 23, 0, 5, 0, 0, 0, 29, 5, 0, 0, 11, 17, 40, 0, 0, 0, 0, 5, 41, 0, 0, 11, 5, 23, 47, 0, 0, 5, 17, 0, 53, 0, 16, 0, 0, 29, 59, 5, 0, 0, 0, 0, 70, 11, 0, 17, 23, 40, 71, 0, 0, 0, 5, 0, 88, 0, 0, 5

Offset

1,5

Links

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

Formula

G.f.: Sum_{k>=1} (6*k - 1)*x^(6*k-1)/(1 - x^(6*k-1)). - Ilya Gutkovskiy, Mar 21 2017

Sum_{k=1..n} a(k) = c * n^2 + O(n*log(n)), where c = Pi^2/72 = 0.137077... (A086729). - Amiram Eldar, Nov 26 2023

Mathematica

Table[Sum[If[Mod[d, 6] == 5, d, 0], {d, Divisors[n]}], {n, 80}] (* Indranil Ghosh, Mar 21 2017 *)
Table[Total[Select[Divisors[n], Mod[#, 6]==5&]], {n, 80}] (* Harvey P. Dale, Dec 30 2017 *)

Prog

(PARI) for(n=1, 80, print1(sumdiv(n, d, if(Mod(d, 6)==5, d, 0)), ", ")) \\ Indranil Ghosh, Mar 21 2017
(Python)
from sympy import divisors
def a(n): return sum([d for d in divisors(n) if d%6==5]) # Indranil Ghosh, Mar 21 2017

Crossrefs

Cf. A086729, A109702.

Cf. Sum_{d|n, d=k-1 mod k} d: A000593 (k=2), A078182 (k=3), A050452 (k=4), A284103 (k=5), this sequence (k=6), A284105 (k=7).

Sequence in context: A005078 A284446 A270030 * A369732 A260911 A228631

Adjacent sequences: A284101 A284102 A284103 * A284105 A284106 A284107

Keyword

nonn,easy

Author

Seiichi Manyama, Mar 20 2017

Status

approved