cp's OEIS Frontend

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.

A343394 Sum of indices of n's distinct prime factors below n.

This page as a plain text file.
%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