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A364063 Expansion of Sum_{k>0} k * x^k / (1 - x^(2*k-1)).

%I A364063 #21 Nov 30 2024 12:29:26
%S A364063 1,3,4,5,8,7,8,14,10,11,18,13,17,22,16,17,26,26,20,30,22,23,42,25,30,
%T A364063 38,28,38,42,31,32,55,44,35,50,37,38,65,50,41,63,43,56,62,46,58,66,62,
%U A364063 50,81,52,53,100,55,56,78,58,74,94,74,68,86,80,65,90,67,82,124,70,71,98,86,92,117,76,77
%N A364063 Expansion of Sum_{k>0} k * x^k / (1 - x^(2*k-1)).
%H A364063 Antti Karttunen, <a href="/A364063/b364063.txt">Table of n, a(n) for n = 1..20000</a>
%F A364063 a(n) = (1/2) * Sum_{d | 2*n-1} (d+1) = A007503(2*n-1)/2.
%F A364063 G.f.: Sum_{k>0} x^k / (1 - x^(2*k-1))^2.
%F A364063 a(n) = A336840(A064216(n)). - _Antti Karttunen_, Nov 30 2024
%t A364063 a[n_] := DivisorSum[2*n - 1, # + 1 &]/2; Array[a, 100] (* _Amiram Eldar_, Jul 04 2023*)
%o A364063 (PARI) a(n) = sumdiv(2*n-1, d, d+1)/2;
%Y A364063 Cf. A000005, A000203, A007503, A064216, A336840.
%Y A364063 Cf. A364066, A364085.
%K A364063 nonn
%O A364063 1,2
%A A364063 _Seiichi Manyama_, Jul 04 2023