A284105 a(n) = Sum_{d|n, d == 6 (mod 7)} d.

0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 6, 13, 0, 0, 0, 0, 6, 0, 20, 0, 0, 0, 6, 0, 13, 27, 0, 0, 6, 0, 0, 0, 34, 0, 6, 0, 0, 13, 20, 41, 6, 0, 0, 0, 0, 0, 54, 0, 0, 0, 13, 0, 33, 55, 0, 0, 0, 0, 26, 0, 62, 0, 0, 13, 6, 0, 34, 69, 0, 0, 6, 0, 0, 0, 76, 0, 19, 0, 20, 27, 41

Offset: 1

Author

Seiichi Manyama, Mar 20 2017

Keywords

• nonn
• easy

Links

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

Crossrefs

Cf. A109708.

Cf. Sum_{d|n, d == k-1 (mod k)} d: A000593 (k=2), A078182 (k=3), A050452 (k=4), A284103 (k=5), A284104 (k=6), this sequence (k=7).

Cf. Sum_{d|n, d == k (mod 7)} d: A284099 (k=1), A284443 (k=2), A284444 (k=3), A284445 (k=4), A284446 (k=5), this sequence (k=6).

Programs

Mathematica

Table[Sum[If[Mod[d,7] == 6,d, 0], {d, Divisors[n]}], {n, 82}] (* Indranil Ghosh, Mar 21 2017 *)

PARI

for(n=1, 82, print1(sumdiv(n, d, if(Mod(d,7)==6, 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%7==6]) # Indranil Ghosh, Mar 21 2017

Formula

G.f.: Sum_{k>=1} (7*k - 1)*x^(7*k-1)/(1 - x^(7*k-1)). - Ilya Gutkovskiy, Mar 21 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