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 A347103 #11 Aug 19 2021 15:47:56
%S A347103 0,1,2,-1,3,-1,4,-1,2,-2,5,-3,6,-3,5,-1,7,-1,8,-4,6,-4,9,-3,3,-5,2,-5,
%T A347103 10,-4,11,-1,7,-6,7,-3,12,-7,8,-4,13,-5,14,-6,5,-8,15,-3,4,-2,9,-7,16,
%U A347103 -1,8,-5,10,-9,17,-6,18,-10,6,-1,9,-6,19,-8,11,-6,20,-3
%N A347103 G.f.: Sum_{k>=1} k * x^prime(k) / (1 + x^prime(k)).
%C A347103 a(n) is the sum of indices of prime divisors p|n such that n/p is odd, minus the sum of indices of prime divisors p|n such that n/p is even.
%H A347103 Michael De Vlieger, <a href="/A347103/b347103.txt">Table of n, a(n) for n = 1..10000</a>
%H A347103 <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>
%F A347103 a(n) = -Sum_{p|n, p prime} (-1)^(n/p) * pi(p), where pi = A000720.
%t A347103 nmax = 72; CoefficientList[Series[Sum[k x^Prime[k]/(1 + x^Prime[k]), {k, 1, nmax}], {x, 0, nmax}], x] // Rest
%t A347103 Table[-DivisorSum[n, (-1)^(n/#) PrimePi[#] &, PrimeQ[#] &], {n, 1, 72}]
%o A347103 (PARI) a(n) = my(f=factor(n)[,1]); sum(k=1, #f, if ((n/f[k]) % 2, primepi(f[k]), -primepi(f[k]))); \\ _Michel Marcus_, Aug 19 2021
%Y A347103 Cf. A000720, A066328, A300852, A305614, A332422.
%K A347103 sign
%O A347103 1,3
%A A347103 _Ilya Gutkovskiy_, Aug 18 2021