A359325 - OEIS

%I #16 Aug 16 2023 02:27:04

%S 0,0,1,0,0,1,0,1,1,0,0,1,1,0,1,0,1,2,0,0,1,0,1,1,0,1,1,2,0,1,0,0,2,0,

%T 1,1,0,1,2,0,0,1,2,1,1,0,0,2,0,1,1,0,2,1,0,0,1,2,0,2,1,1,2,0,0,1,0,1,

%U 1,0,1,2,2,0,1,0,1,2,0,1,2,0,2,1,0,0,1,2,1,1

%N Number of divisors of 6*n-3 of form 6*k+5.

%H Seiichi Manyama, <a href="/A359325/b359325.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) = A319995(6*n-3).

%F G.f.: Sum_{k>0} x^(3*k)/(1 - x^(6*k-1)).

%F G.f.: Sum_{k>0} x^(5*k-2)/(1 - x^(6*k-3)).

%t a[n_] := DivisorSum[6*n-3, 1 &, Mod[#, 6] == 5 &]; Array[a, 100] (* _Amiram Eldar_, Aug 16 2023 *)

%o (PARI) a(n) = sumdiv(6*n-3, d, d%6==5);

%o (PARI) my(N=100, x='x+O('x^N)); concat([0, 0], Vec(sum(k=1, N, x^(3*k)/(1-x^(6*k-1)))))

%o (PARI) my(N=100, x='x+O('x^N)); concat([0, 0], Vec(sum(k=1, N, x^(5*k-2)/(1-x^(6*k-3)))))

%Y Cf. A319995, A359305, A359324, A359326, A359327.

%K nonn,easy

%O 1,18

%A _Seiichi Manyama_, Dec 25 2022