A284361 a(n) = Sum_{d|n, d = 0, 1, or 4 mod 5} d.

1, 1, 1, 5, 6, 7, 1, 5, 10, 16, 12, 11, 1, 15, 21, 21, 1, 16, 20, 40, 22, 12, 1, 35, 31, 27, 10, 19, 30, 67, 32, 21, 12, 35, 41, 56, 1, 20, 40, 80, 42, 42, 1, 60, 75, 47, 1, 51, 50, 91, 52, 31, 1, 70, 72, 75, 20, 30, 60, 151, 62, 32, 31, 85, 71, 84, 1, 39, 70, 135

Offset: 1

Author

Seiichi Manyama, Mar 25 2017

Keywords

• nonn

Links

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

Crossrefs

Cf. A036820 (1/f(-x, -x^4)), A113429 (f(-x, -x^4)), A102753.

Cf. Sum_{d|n, d = 0, 1, or k-1 mod k} d: A000203 (k=3), this sequence (k=5), A284362 (k=6), A284363 (k=7), A284372 (k=12).

Programs

Mathematica

Table[Sum[If[Mod[d, 5]<2 || Mod[d, 5]==4, d, 0], {d, Divisors[n]}], {n, 80}] (* Indranil Ghosh, Mar 25 2017 *)
Table[Total[Select[Divisors[n],MemberQ[{0,1,4},Mod[#,5]]&]],{n,70}] (* Harvey P. Dale, Aug 02 2020 *)

PARI

a(n) = sumdiv(n, d, ((d + 1) % 5 < 3) * d); \\ Amiram Eldar, Apr 12 2024

Formula

Sum_{k=1..n} a(k) ~ c * n^2, where c = Pi^2/20 = A102753 / 10 = 0.4934802... . - Amiram Eldar, Apr 12 2024