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 A359236 Number of divisors of 5*n-2 of form 5*k+1. 10

%I #24 Aug 23 2023 08:42:00

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

%T 1,1,2,1,1,4,1,3,2,1,1,3,1,1,2,2,2,3,1,1,3,1,1,5,1,1,2,2,1,3,1,2,2,2,

%U 1,3,1,1,3,3,1,4,1,1,2,1,2,4,1,2,2,1,1,3,1,3

%N Number of divisors of 5*n-2 of form 5*k+1.

%C Also number of divisors of 5*n-2 of form 5*k+3.

%H Seiichi Manyama, <a href="/A359236/b359236.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) = A001876(5*n-2) = A001878(5*n-2).

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

%F G.f.: Sum_{k>0} x^(3*k-2)/(1 - x^(5*k-4)).

%t a[n_] := DivisorSum[5*n-2, 1 &, Mod[#, 5] == 1 &]; Array[a, 100] (* _Amiram Eldar_, Aug 23 2023 *)

%o (PARI) a(n) = sumdiv(5*n-2, d, d%5==1);

%o (PARI) a(n) = sumdiv(5*n-2, d, d%5==3);

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

%o (PARI) my(N=100, x='x+O('x^N)); Vec(sum(k=1, N, x^(3*k-2)/(1-x^(5*k-4))))

%Y Cf. A001876, A001878, A359233, A359237, A359238.

%K nonn,easy

%O 1,4

%A _Seiichi Manyama_, Dec 22 2022

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Last modified October 4 15:50 EDT 2023. Contains 365885 sequences. (Running on oeis4.)