A359244 - OEIS

%I #16 Aug 16 2023 02:27:13

%S 0,1,0,1,1,1,0,2,0,1,1,2,0,2,0,1,1,1,1,3,0,1,1,1,0,3,0,2,1,1,0,3,1,1,

%T 1,2,0,2,0,2,1,1,0,4,1,1,2,1,0,2,0,2,1,2,0,3,0,2,1,2,1,3,0,1,1,1,0,5,

%U 0,1,2,1,0,2,1,2,1,1,1,4,0,2,1,3,0,2,0,1,2,1

%N Number of divisors of 5*n-4 of form 5*k+2.

%C Also number of divisors of 5*n-4 of form 5*k+3.

%H Seiichi Manyama, <a href="/A359244/b359244.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) = A001877(5*n-4) = A001878(5*n-4).

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

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

%t a[n_] := DivisorSum[5*n-4, 1 &, Mod[#, 5] == 2 &]; Array[a, 100] (* _Amiram Eldar_, Aug 16 2023 *)

%o (PARI) a(n) = sumdiv(5*n-4, d, d%5==2);

%o (PARI) a(n) = sumdiv(5*n-4, d, d%5==3);

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

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

%Y Cf. A001877, A001878.

%K nonn,easy

%O 1,8

%A _Seiichi Manyama_, Dec 22 2022