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A330018 a(n) = Sum_{d|n} (bigomega(d) - omega(d)).

%I A330018 #10 Jun 13 2020 00:50:13
%S A330018 0,0,0,1,0,0,0,3,1,0,0,2,0,0,0,6,0,2,0,2,0,0,0,6,1,0,3,2,0,0,0,10,0,0,
%T A330018 0,6,0,0,0,6,0,0,0,2,2,0,0,12,1,2,0,2,0,6,0,6,0,0,0,4,0,0,2,15,0,0,0,
%U A330018 2,0,0,0,13,0,0,2,2,0,0,0,12,6,0,0,4,0,0,0,6,0,4
%N A330018 a(n) = Sum_{d|n} (bigomega(d) - omega(d)).
%C A330018 Inverse Moebius transform of A046660.
%H A330018 Robert Israel, <a href="/A330018/b330018.txt">Table of n, a(n) for n = 1..10000</a>
%F A330018 G.f.: Sum_{k>=1} A046660(k) * x^k / (1 - x^k).
%F A330018 a(n) = A069264(n) - A062799(n).
%F A330018 If m and n are coprime, a(m*n) = tau(m)*a(n) + tau(n)*a(m), where tau = A000005. - _Robert Israel_, Jun 12 2020
%p A330018 N:= 100: # for a(1)..a(N)
%p A330018 V:= Vector(N):
%p A330018 for d from 1 to N do
%p A330018   v:= add(t[2]-1, t=ifactors(d)[2]);
%p A330018   L:= [seq(i,i=d..N,d)]:
%p A330018   V[L]:= map(`+`,V[L],v);
%p A330018 od:
%p A330018 convert(V,list); # _Robert Israel_, Jun 12 2020
%t A330018 a[n_] := Sum[PrimeOmega[d] - PrimeNu[d], {d, Divisors[n]}]; Table[a[n], {n, 1, 90}]
%o A330018 (PARI) a(n) = sumdiv(n, d, bigomega(d) - omega(d)); \\ _Michel Marcus_, Jun 12 2020
%Y A330018 Cf. A001221, A001222, A005117 (positions of 0's), A046660, A062799, A069264, A268340.
%K A330018 nonn
%O A330018 1,8
%A A330018 _Ilya Gutkovskiy_, Nov 27 2019