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%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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