A284363 a(n) = Sum_{d|n, d = 0, 1, or 6 mod 7} d.

1, 1, 1, 1, 1, 7, 8, 9, 1, 1, 1, 7, 14, 22, 16, 9, 1, 7, 1, 21, 29, 23, 1, 15, 1, 14, 28, 50, 30, 22, 1, 9, 1, 35, 43, 43, 1, 1, 14, 29, 42, 91, 44, 23, 16, 1, 1, 63, 57, 51, 1, 14, 1, 34, 56, 114, 58, 30, 1, 42, 1, 63, 92, 73, 14, 29, 1, 35, 70, 127, 72, 51, 1, 1

Offset: 1

Author

Seiichi Manyama, Mar 25 2017

Keywords

• nonn

Links

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

Crossrefs

Cf. A232714.

Cf. Sum_{d|n, d = 0, 1, or k-1 mod k} d: A000203 (k=3), A284361 (k=5), A284362 (k=6), this sequence (k=7), A284372 (k=12).

Programs

Mathematica

Table[Sum[If[Mod[d, 7] <2 || Mod[d, 7]==6, d, 0], {d, Divisors[n]}], {n, 80}] (* Indranil Ghosh, Mar 25 2017 *)

PARI

a(n) = sumdiv(n, d, ((d + 1) % 7 < 3) * d); \\ Amiram Eldar, Apr 12 2024

Formula

Sum_{k=1..n} a(k) ~ c * n^2, where c = Pi^2/28 = 0.352485... . - Amiram Eldar, Apr 12 2024