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A371629
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If 2n = Sum 2^e(k) then a(n) = Sum e(k)^3.
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1
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1, 8, 9, 27, 28, 35, 36, 64, 65, 72, 73, 91, 92, 99, 100, 125, 126, 133, 134, 152, 153, 160, 161, 189, 190, 197, 198, 216, 217, 224, 225, 216, 217, 224, 225, 243, 244, 251, 252, 280, 281, 288, 289, 307, 308, 315, 316, 341, 342, 349, 350, 368, 369, 376, 377, 405, 406, 413, 414, 432
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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.: (1/(1 - x)) * Sum_{k>=0} (k+1)^3 * x^(2^k) / (1 + x^(2^k)).
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EXAMPLE
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To get a(5), we write 10 = 2 + 8 = 2^1 + 2^3 so a(5) = 1^3 + 3^3 = 28.
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MATHEMATICA
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a[n_] := Total[Flatten[Position[Reverse[IntegerDigits[n, 2]], 1]]^3]; Table[a[n], {n, 1, 60}]
nmax = 60; CoefficientList[Series[(1/(1 - x)) Sum[(k + 1)^3 x^(2^k)/(1 + x^(2^k)), {k, 0, Log[2, nmax]}], {x, 0, nmax}], x] // Rest
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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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