A284446 a(n) = Sum_{d|n, d == 5 (mod 7)} d.

0, 0, 0, 0, 5, 0, 0, 0, 0, 5, 0, 12, 0, 0, 5, 0, 0, 0, 19, 5, 0, 0, 0, 12, 5, 26, 0, 0, 0, 5, 0, 0, 33, 0, 5, 12, 0, 19, 0, 45, 0, 0, 0, 0, 5, 0, 47, 12, 0, 5, 0, 26, 0, 54, 5, 0, 19, 0, 0, 17, 61, 0, 0, 0, 5, 33, 0, 68, 0, 5, 0, 12, 0, 0, 80, 19, 0, 26, 0, 45, 0, 82

Offset: 1

Author

Seiichi Manyama, Mar 27 2017

Keywords

• nonn
• easy

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A109707.

Cf. Sum_{d|n, d == k (mod 7)} d: A284099 (k=1), A284443 (k=2), A284444 (k=3), A284445 (k=4), this sequence (k=5), A284105 (k=6).

Programs

Maple

f:= n -> convert(select(t -> t mod 7 = 5, numtheory:-divisors(n)),`+`):
map(f, [$1..1000]); # Robert Israel, Mar 27 2017

Mathematica

Table[DivisorSum[n, # &, Mod[#, 7] == 5 &], {n, 82}] (* Giovanni Resta, Mar 27 2017 *)

PARI

for(n=1, 82, print1(sumdiv(n, d, if(Mod(d, 7)==5, d, 0)), ", ")) \\ Indranil Ghosh, Mar 27 2017

Formula

G.f.: Sum_{k>=0} (5+7k) x^(5+7k)/(1-x^(5+7k)). - Robert Israel, Mar 27 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