A357912 - OEIS

%I #22 Aug 09 2023 00:52:58

%S 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,

%T 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,

%U 1,1,68,35,24,1,1,13,1,1,1,1,1,79,1,1,1,1,1,13,1

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

%H Seiichi Manyama, <a href="/A357912/b357912.txt">Table of n, a(n) for n = 1..10000</a>

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

%t a[n_] := DivisorSum[n, # &, Mod[#, 11] == 1 &]; Array[a, 100] (* _Amiram Eldar_, Aug 09 2023 *)

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

%o (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))))

%Y 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).

%Y Cf. A357911.

%K nonn

%O 1,12

%A _Seiichi Manyama_, Jan 17 2023