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 A372620 #5 May 08 2024 08:52:41
%S A372620 0,2,6,2,15,8,28,2,6,17,55,8,78,30,21,2,119,8,152,17,34,57,207,8,15,
%T A372620 80,6,30,290,23,341,2,61,121,43,8,444,154,84,17,533,36,602,57,21,209,
%U A372620 705,8,28,17,125,80,848,8,70,30,158,292,1003,23,1098,343,34,2,93
%N A372620 Expansion of Sum_{k>=1} k * prime(k) * x^prime(k) / (1 - x^prime(k)).
%H A372620 <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>
%F A372620 L.g.f.: -log( Product_{k>=1} (1 - x^prime(k))^k ).
%F A372620 If n = Product (p_j^k_j) then a(n) = Sum (pi(p_j) * p_j), where pi = A000720.
%e A372620 a(60) = a(2^2 * 3 * 5) = a(prime(1)^2 * prime(2) * prime(3)) = 1 * 2 + 2 * 3 + 3 * 5 = 23.
%t A372620 nmax = 65; CoefficientList[Series[Sum[k Prime[k] x^Prime[k]/(1 - x^Prime[k]), {k, 1, nmax}], {x, 0, nmax}], x] // Rest
%t A372620 a[n_] := Plus @@ (PrimePi[#[[1]]] #[[1]] & /@ FactorInteger[n]); Table[a[n], {n, 1, 65}]
%Y A372620 Cf. A000720, A001414, A005063, A008472, A056239, A061150, A066328, A328639.
%K A372620 nonn
%O A372620 1,2
%A A372620 _Ilya Gutkovskiy_, May 07 2024