A284281 a(n) = Sum_{d|n, d == 3 (mod 5)} d.

0, 0, 3, 0, 0, 3, 0, 8, 3, 0, 0, 3, 13, 0, 3, 8, 0, 21, 0, 0, 3, 0, 23, 11, 0, 13, 3, 28, 0, 3, 0, 8, 36, 0, 0, 21, 0, 38, 16, 8, 0, 3, 43, 0, 3, 23, 0, 59, 0, 0, 3, 13, 53, 21, 0, 36, 3, 58, 0, 3, 0, 0, 66, 8, 13, 36, 0, 68, 26, 0, 0, 29, 73, 0, 3, 38, 0, 94, 0, 8

Offset

1,3

Links

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

Formula

G.f.: Sum_{k>=0} (5*k + 3)*x^(5*k+3)/(1 - x^(5*k+3)). - Ilya Gutkovskiy, Mar 25 2017

Sum_{k=1..n} a(k) = c * n^2 + O(n*log(n)), where c = Pi^2/60 = 0.164493... (A013661 / 10). - Amiram Eldar, Nov 26 2023

Mathematica

Table[Sum[If[Mod[d, 5] == 3, d, 0], {d, Divisors[n]}], {n, 80}] (* Indranil Ghosh, Mar 24 2017 *)

Prog

(PARI) for(n=1, 82, print1(sumdiv(n, d, if(Mod(d, 5)==3, d, 0)), ", ")) \\ Indranil Ghosh, Mar 24 2017
(Python)
from sympy import divisors
def a(n): return sum([d for d in divisors(n) if d%5==3]) # Indranil Ghosh, Mar 24 2017

Crossrefs

Cf. A013661, A109699, A284152.

Cf. Sum_{d|n, d=k mod 5} d: A284097 (k=1), A284280 (k=2), this sequence (k=3), A284103 (k=4).

Sequence in context: A272974 A063691 A359967 * A075874 A181634 A230652

Adjacent sequences: A284278 A284279 A284280 * A284282 A284283 A284284

Keyword

nonn,easy

Author

Seiichi Manyama, Mar 24 2017

Status

approved