A284280 a(n) = Sum_{d|n, d == 2 (mod 5)} d.

0, 2, 0, 2, 0, 2, 7, 2, 0, 2, 0, 14, 0, 9, 0, 2, 17, 2, 0, 2, 7, 24, 0, 14, 0, 2, 27, 9, 0, 2, 0, 34, 0, 19, 7, 14, 37, 2, 0, 2, 0, 51, 0, 24, 0, 2, 47, 14, 7, 2, 17, 54, 0, 29, 0, 9, 57, 2, 0, 14, 0, 64, 7, 34, 0, 24, 67, 19, 0, 9, 0, 86, 0, 39, 0, 2, 84, 2, 0, 2

Offset: 1

Author

Seiichi Manyama, Mar 24 2017

Keywords

• nonn
• easy

Links

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

Crossrefs

Cf. A013661, A109698, A284152.

Cf. Sum_{d|n, d=k mod 5} d: A284097 (k=1), this sequence (k=2), A284281 (k=3), A284103 (k=4).

Programs

Mathematica

Table[Sum[If[Mod[d, 5] == 2, d, 0], {d, Divisors[n]}], {n, 80}] (* Indranil Ghosh, Mar 24 2017 *)

PARI

for(n=1, 80, print1(sumdiv(n, d, if(Mod(d, 5)==2, 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==2]) # Indranil Ghosh, Mar 24 2017

Formula

G.f.: Sum_{k>=0} (5*k + 2)*x^(5*k+2)/(1 - x^(5*k+2)). - 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