Search: a364034 -id:a364034
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A364035
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Expansion of Sum_{k>0} k * x^k / (1 - 2*x^(2*k)).
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+10
1
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1, 2, 5, 4, 9, 10, 15, 8, 31, 18, 43, 20, 77, 30, 165, 16, 273, 62, 531, 36, 1083, 86, 2071, 40, 4141, 154, 8285, 60, 16413, 330, 32799, 32, 65687, 546, 131175, 124, 262181, 1062, 524545, 72, 1048617, 2166, 2097195, 172, 4194879, 4142, 8388655, 80, 16777321, 8282, 33555285, 308
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OFFSET
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1,2
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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))^2.
a(n) = Sum_{d|n, d odd} 2^((d-1)/2) * (n/d).
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MATHEMATICA
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a[n_] := DivisorSum[n, 2^((#-1)/2) * (n/#) &, 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)*n/d);
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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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