A363903 - OEIS

%I #17 Jun 29 2023 08:58:08

%S 1,1,1,1,3,1,1,1,4,3,1,1,5,1,3,1,6,4,1,3,7,1,1,1,10,5,4,1,9,3,1,1,10,

%T 6,3,4,11,1,5,3,12,7,1,1,18,1,1,1,14,10,6,5,15,4,3,1,16,9,1,3,17,1,10,

%U 1,24,10,1,6,19,3,1,4,20,11,10,1,21,5,1,3,25,12,1,7,30,1,9,1,24,18,5,1,25,1,3,1

%N Expansion of Sum_{k>0} x^k / (1 - x^(4*k))^2.

%H Seiichi Manyama, <a href="/A363903/b363903.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) = (1/4) * Sum_{d|n, d==1 mod 4} (d+3) = (3 * A001826(n) + A050449(n))/4.

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

%t a[n_] := DivisorSum[n, # + 3 &, Mod[#, 4] == 1 &]/4; Array[a, 100] (* _Amiram Eldar_, Jun 27 2023 *)

%o (PARI) a(n) = sumdiv(n, d, (d%4==1)*(d+3))/4;

%Y Cf. A363901, A363925.

%Y Cf. A001826, A050449.

%K nonn

%O 1,5

%A _Seiichi Manyama_, Jun 27 2023