A363804 a(n) = Sum_{d|n, d == 0, 3, or 4 mod 7} d.

0, 0, 3, 4, 0, 3, 7, 4, 3, 10, 11, 7, 0, 21, 3, 4, 17, 21, 0, 14, 31, 11, 0, 31, 25, 0, 3, 53, 0, 13, 31, 36, 14, 17, 42, 25, 0, 38, 42, 14, 0, 87, 0, 15, 48, 46, 0, 31, 56, 35, 20, 56, 53, 21, 11, 109, 3, 0, 59, 77, 0, 31, 94, 36, 0, 80, 67, 21, 3, 136, 0, 49, 73, 74, 28, 42, 95, 42, 0, 94, 84, 0, 0

Offset: 1

Author

Seiichi Manyama, Jun 23 2023

Keywords

• nonn
• easy

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A284363, A284444, A284445, A363803.

Cf. A363801.

Programs

Mathematica

a[n_] := DivisorSum[n, # &, MemberQ[{0, 3, 4}, Mod[#, 7]] &]; Array[a, 100] (* Amiram Eldar, Jun 23 2023 *)
sm7[n_]:=Total[Select[Divisors[n],MemberQ[{0,3,4},Mod[#,7]]&]]; Array[sm7,100] (* Harvey P. Dale, Sep 11 2024 *)

PARI

my(N=90, x='x+O('x^N)); concat([0, 0], Vec(sum(k=1, N, [1, 0, 0, 1, 1, 0, 0][k%7+1]*k*x^k/(1-x^k))))

Formula

G.f.: Sum_{k>0, k == 0, 3 or 4 mod 7} k * x^k/(1 - x^k).