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Number of divisors of 6*n-5 of form 6*k+1.
6

%I #15 Aug 16 2023 02:27:01

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

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

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

%N Number of divisors of 6*n-5 of form 6*k+1.

%H Seiichi Manyama, <a href="/A359309/b359309.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) = A279060(6*n-5).

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

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

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

%Y Cf. A279060, A359305, A359306, A359307, A359308.

%K nonn,easy

%O 1,2

%A _Seiichi Manyama_, Dec 25 2022