This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A371629 #7 May 27 2024 22:58:48
%S A371629 1,8,9,27,28,35,36,64,65,72,73,91,92,99,100,125,126,133,134,152,153,
%T A371629 160,161,189,190,197,198,216,217,224,225,216,217,224,225,243,244,251,
%U A371629 252,280,281,288,289,307,308,315,316,341,342,349,350,368,369,376,377,405,406,413,414,432
%N A371629 If 2n = Sum 2^e(k) then a(n) = Sum e(k)^3.
%F A371629 G.f.: (1/(1 - x)) * Sum_{k>=0} (k+1)^3 * x^(2^k) / (1 + x^(2^k)).
%e A371629 To get a(5), we write 10 = 2 + 8 = 2^1 + 2^3 so a(5) = 1^3 + 3^3 = 28.
%t A371629 a[n_] := Total[Flatten[Position[Reverse[IntegerDigits[n, 2]], 1]]^3]; Table[a[n], {n, 1, 60}]
%t A371629 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
%Y A371629 Cf. A003997, A008935, A029931.
%K A371629 nonn
%O A371629 1,2
%A A371629 _Ilya Gutkovskiy_, May 24 2024