cp's OEIS Frontend

A332424 If n = Product (p_j^k_j) then a(n) = Sum ((-1)^(pi(p_j) + 1) * p_j), where pi = A000720.

%I A332424 #7 Feb 13 2020 02:53:57
%S A332424 0,2,-3,2,5,-1,-7,2,-3,7,11,-1,-13,-5,2,2,17,-1,-19,7,-10,13,23,-1,5,
%T A332424 -11,-3,-5,-29,4,31,2,8,19,-2,-1,-37,-17,-16,7,41,-8,-43,13,2,25,47,
%U A332424 -1,-7,7,14,-11,-53,-1,16,-5,-22,-27,59,4,-61,33,-10,2,-8,10,67,19,20
%N A332424 If n = Product (p_j^k_j) then a(n) = Sum ((-1)^(pi(p_j) + 1) * p_j), where pi = A000720.
%C A332424 Sum of distinct prime factors of n with odd indices minus the sum of distinct prime factors of n with even indices.
%H A332424 <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>
%F A332424 G.f.: Sum_{k>=1} (-1)^(k + 1) * prime(k) * x^prime(k) / (1 - x^prime(k)).
%F A332424 L.g.f.: log(Product_{k>=1} (1 - x^prime(k))^((-1)^k)).
%e A332424 a(66) = a(2 * 3 * 11) = a(prime(1) * prime(2) * prime(5)) = 2 - 3 + 11 = 10.
%t A332424 a[n_] := Plus @@ ((-1)^(PrimePi[#[[1]]] + 1) #[[1]] & /@ FactorInteger[n]); a[1] = 0; Table[a[n], {n, 1, 69}]
%t A332424 nmax = 69; CoefficientList[Series[Sum[(-1)^(k + 1) Prime[k] x^Prime[k]/(1 - x^Prime[k]), {k, 1, nmax}], {x, 0, nmax}], x] // Rest
%Y A332424 Cf. A000720, A002129, A008472, A071321, A112798, A195017, A325699, A332422, A332425.
%K A332424 sign
%O A332424 1,2
%A A332424 _Ilya Gutkovskiy_, Feb 12 2020