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A364034
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Expansion of Sum_{k>0} x^k / (1 - 2*x^(2*k)).
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1
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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
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OFFSET
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1,3
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LINKS
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FORMULA
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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).
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MATHEMATICA
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a[n_] := DivisorSum[n, 2^((#-1)/2) &, OddQ[#] &]; Array[a, 50] (* Amiram Eldar, Jul 02 2023 *)
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PROG
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(PARI) a(n) = sumdiv(n, d, (d%2==1)*2^((d-1)/2));
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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