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%I A364035 #11 Jul 02 2023 09:01:04
%S A364035 1,2,5,4,9,10,15,8,31,18,43,20,77,30,165,16,273,62,531,36,1083,86,
%T A364035 2071,40,4141,154,8285,60,16413,330,32799,32,65687,546,131175,124,
%U A364035 262181,1062,524545,72,1048617,2166,2097195,172,4194879,4142,8388655,80,16777321,8282,33555285,308
%N A364035 Expansion of Sum_{k>0} k * x^k / (1 - 2*x^(2*k)).
%F A364035 G.f.: Sum_{k>0} 2^(k-1) * x^(2*k-1) / (1 - x^(2*k-1))^2.
%F A364035 a(n) = Sum_{d|n, d odd} 2^((d-1)/2) * (n/d).
%t A364035 a[n_] := DivisorSum[n, 2^((#-1)/2) * (n/#) &, OddQ[#] &]; Array[a, 50] (* _Amiram Eldar_, Jul 02 2023 *)
%o A364035 (PARI) a(n) = sumdiv(n, d, (d%2==1)*2^((d-1)/2)*n/d);
%Y A364035 Cf. A002131, A364034.
%K A364035 nonn
%O A364035 1,2
%A A364035 _Seiichi Manyama_, Jul 02 2023

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