A357912 a(n) = Sum_{d|n, d==1 (mod 11)} d.

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 13, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 24, 13, 1, 1, 1, 1, 1, 1, 1, 1, 1, 35, 1, 13, 1, 1, 1, 1, 1, 1, 1, 1, 46, 24, 1, 13, 1, 1, 1, 1, 1, 1, 1, 57, 1, 1, 1, 13, 1, 1, 1, 1, 1, 1, 68, 35, 24, 1, 1, 13, 1, 1, 1, 1, 1, 79, 1, 1, 1, 1, 1, 13, 1

Offset: 1

Author

Seiichi Manyama, Jan 17 2023

Keywords

• nonn

Links

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

Crossrefs

Cf. Sum_{d|n, d==1 (mod k)} d: A000593 (k=2), A078181 (k=3), A050449 (k=4), A284097 (k=5), A284098 (k=6), A284099 (k=7), A284100 (k=8), this sequence (k=11).

Cf. A357911.

Programs

Mathematica

a[n_] := DivisorSum[n, # &, Mod[#, 11] == 1 &]; Array[a, 100] (* Amiram Eldar, Aug 09 2023 *)

PARI

a(n) = sumdiv(n, d, (Mod(d, 11)==1)*d);

PARI

my(N=100, x='x+O('x^N)); Vec(sum(k=0, N, (11*k+1)*x^(11*k+1)/(1-x^(11*k+1))))

Formula

G.f.: Sum_{k>=0} (11*k+1) * x^(11*k+1)/(1 - x^(11*k+1)).