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 A343394 #4 Apr 13 2021 19:23:40 %S A343394 0,0,0,1,0,3,0,1,2,4,0,3,0,5,5,1,0,3,0,4,6,6,0,3,3,7,2,5,0,6,0,1,7,8, %T A343394 7,3,0,9,8,4,0,7,0,6,5,10,0,3,4,4,9,7,0,3,8,5,10,11,0,6,0,12,6,1,9,8, %U A343394 0,8,11,8,0,3,0,13,5,9,9,9,0,4,2,14,0,7,10,15,12,6,0,6 %N A343394 Sum of indices of n's distinct prime factors below n. %H A343394 <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a> %F A343394 G.f.: Sum_{k>=1} k * x^(2*prime(k)) / (1 - x^prime(k)). %F A343394 a(n) = 0 if n is prime, A066328(n) otherwise. %e A343394 a(7) = a(prime(4)) = 0. %e A343394 a(21) = a(3 * 7) = a(prime(2) * prime(4)) = 2 + 4 = 6. %t A343394 nmax = 90; CoefficientList[Series[Sum[k x^(2 Prime[k])/(1 - x^Prime[k]), {k, 1, nmax}], {x, 0, nmax}], x] // Rest %t A343394 a[n_] := If[PrimeQ[n], 0, Plus @@ (PrimePi[#[[1]]] & /@ FactorInteger[n])]; Table[a[n], {n, 90}] %Y A343394 Cf. A066328, A087624, A105221. %K A343394 nonn %O A343394 1,6 %A A343394 _Ilya Gutkovskiy_, Apr 13 2021