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 A384816 #7 Jun 16 2025 19:14:43
%S A384816 0,1,8,1,27,9,64,1,8,28,125,9,216,65,35,1,343,9,512,28,72,126,729,9,
%T A384816 27,217,8,65,1000,36,1331,1,133,344,91,9,1728,513,224,28,2197,73,2744,
%U A384816 126,35,730,3375,9,64,28,351,217,4096,9,152,65,520,1001,4913,36,5832,1332,72,1,243,134,6859,344,737,92
%N A384816 Sum of the cubes of the indices of distinct prime factors of n.
%H A384816 <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>.
%F A384816 If n = Product (p_j^k_j) then a(n) = Sum (pi(p_j)^3), where pi = A000720.
%F A384816 G.f.: Sum_{k>=1} k^3 * x^prime(k) / (1 - x^prime(k)).
%t A384816 Table[Plus @@ (PrimePi[#[[1]]]^3 & /@ FactorInteger[n]), {n, 70}]
%t A384816 nmax = 70; CoefficientList[Series[Sum[k^3 x^Prime[k]/(1 - x^Prime[k]), {k, 1, nmax}], {x, 0, nmax}], x] // Rest
%o A384816 (PARI) a(n) = my(f=factor(n)[,1]); sum(k=1, #f~, primepi(f[k])^3); \\ _Michel Marcus_, Jun 10 2025
%Y A384816 Cf. A000720, A005064, A066328, A332385.
%K A384816 nonn
%O A384816 1,3
%A A384816 _Ilya Gutkovskiy_, Jun 10 2025