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 A333842 #17 Jul 25 2024 03:11:58
%S A333842 0,0,0,1,0,0,0,1,2,0,0,1,0,0,0,1,0,2,0,1,0,0,0,1,3,0,2,1,0,0,0,1,0,0,
%T A333842 0,3,0,0,0,1,0,0,0,1,2,0,0,1,4,3,0,1,0,2,0,1,0,0,0,1,0,0,2,1,0,0,0,1,
%U A333842 0,0,0,3,0,0,3,1,0,0,0,1,2,0,0,1,0,0,0,1,0,2,0,1,0,0,0,1,0,4,2,4,0,0,0,1
%N A333842 G.f.: Sum_{k>=1} k * x^(prime(k)^2) / (1 - x^(prime(k)^2)).
%C A333842 Sum of indices of non-unitary prime factors of n (prime factors for which the exponent exceeds 1).
%H A333842 Antti Karttunen, <a href="/A333842/b333842.txt">Table of n, a(n) for n = 1..65537</a>
%H A333842 <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>.
%F A333842 a(n) = A056239(A071773(n)) = A066328(A003557(n)). - _Peter Munn_ and _Antti Karttunen_, Jun 13 2020
%F A333842 Additive with a(p^e) = primepi(p) = A000720(p) if e >= 2, and 0 otherwise. - _Amiram Eldar_, Jul 24 2024
%e A333842 a(450) = a(2 * 3^2 * 5^2) = a(prime(1) * prime(2)^2 * prime(3)^2) = 2 + 3 = 5.
%t A333842 nmax = 104; CoefficientList[Series[Sum[k x^(Prime[k]^2)/(1 - x^(Prime[k]^2)), {k, 1, nmax}], {x,0, nmax}], x] // Rest
%t A333842 f[p_, e_] := If[e == 1, 0, PrimePi[p]]; a[1] = 0; a[n_] := Plus @@ f @@@ FactorInteger[n]; Array[a, 100] (* _Amiram Eldar_, Jul 24 2024 *)
%o A333842 (PARI) A333842(n) = { my(f=factor(n)); sum(k=1, #f~, if(1==f[k, 2],0,1)*primepi(f[k, 1])); }; \\ _Antti Karttunen_, Jun 12 2020
%Y A333842 Cf. A000720, A003557, A005117 (positions of 0's), A056170, A056239, A063958, A066328, A071773.
%K A333842 nonn
%O A333842 1,9
%A A333842 _Ilya Gutkovskiy_, Apr 07 2020