A359308 - OEIS

%I #15 Aug 16 2023 02:26:57

%S 1,1,2,1,2,1,2,1,2,2,2,1,2,1,2,1,3,2,2,1,2,1,2,2,2,2,2,1,2,1,4,1,2,2,

%T 2,1,2,2,2,1,2,2,2,2,4,1,2,1,2,2,2,2,2,1,2,1,3,2,4,1,2,1,2,2,2,3,2,1,

%U 2,2,2,1,4,2,2,1,2,1,2,2,2,2,4,2,2,1,4,1,2,2

%N Number of divisors of 6*n-4 of form 6*k+1.

%H Seiichi Manyama, <a href="/A359308/b359308.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) = A279060(6*n-4).

%F G.f.: Sum_{k>0} x^k/(1 - x^(6*k-4)).

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

%t a[n_] := DivisorSum[6*n-4, 1 &, Mod[#, 6] == 1 &]; Array[a, 100] (* _Amiram Eldar_, Aug 16 2023 *)

%o (PARI) a(n) = sumdiv(6*n-4, d, d%6==1);

%o (PARI) my(N=100, x='x+O('x^N)); Vec(sum(k=1, N, x^k/(1-x^(6*k-4))))

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

%Y Cf. A279060, A359305, A359306, A359307, A359309.

%K nonn,easy

%O 1,3

%A _Seiichi Manyama_, Dec 25 2022