A371629 If 2n = Sum 2^e(k) then a(n) = Sum e(k)^3.

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

Offset: 1

Author

Ilya Gutkovskiy, May 24 2024

Keywords

• nonn

Examples

			To get a(5), we write 10 = 2 + 8 = 2^1 + 2^3 so a(5) = 1^3 + 3^3 = 28.
		

Crossrefs

Cf. A003997, A008935, A029931.

Programs

Mathematica

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

Formula

G.f.: (1/(1 - x)) * Sum_{k>=0} (k+1)^3 * x^(2^k) / (1 + x^(2^k)).