A364034 Expansion of Sum_{k>0} x^k / (1 - 2*x^(2*k)).

1, 1, 3, 1, 5, 3, 9, 1, 19, 5, 33, 3, 65, 9, 135, 1, 257, 19, 513, 5, 1035, 33, 2049, 3, 4101, 65, 8211, 9, 16385, 135, 32769, 1, 65571, 257, 131085, 19, 262145, 513, 524355, 5, 1048577, 1035, 2097153, 33, 4194455, 2049, 8388609, 3, 16777225, 4101, 33554691, 65, 67108865, 8211, 134217765, 9

Offset

1,3

Links

Table of n, a(n) for n=1..56.

Formula

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

a(n) = Sum_{d|n, d odd} 2^((d-1)/2).

Mathematica

a[n_] := DivisorSum[n, 2^((#-1)/2) &, OddQ[#] &]; Array[a, 50] (* Amiram Eldar, Jul 02 2023 *)

Prog

(PARI) a(n) = sumdiv(n, d, (d%2==1)*2^((d-1)/2));

Crossrefs

Cf. A001227, A364035.

Sequence in context: A227361 A318726 A333871 * A373079 A212641 A195835

Adjacent sequences: A364031 A364032 A364033 * A364035 A364036 A364037

Keyword

nonn

Author

Seiichi Manyama, Jul 02 2023

Status

approved