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%I #11 Jun 05 2022 23:20:05
%S 1,-2,-2,1,-2,4,-2,-1,1,4,-2,-2,-2,4,4,2,-2,-2,-2,-2,4,4,-2,2,1,4,-1,
%T -2,-2,-8,-2,-3,4,4,4,1,-2,4,4,2,-2,-8,-2,-2,-2,4,-2,-4,1,-2,4,-2,-2,
%U 2,4,2,4,4,-2,4,-2,4,-2,7,4,-8,-2,-2,4,-8,-2,-1,-2,4,-2,-2,4,-8,-2,-4,2,4,-2,4,4,4,4,2,-2,4,4
%N Dirichlet inverse of A181819, prime shadow of n.
%C Multiplicative because A181819 is.
%H Antti Karttunen, <a href="/A354349/b354349.txt">Table of n, a(n) for n = 1..65537</a>
%F a(1) = 1, and for n > 1, a(n) = -Sum_{d|n, d < n} A181819(n/d) * a(d).
%o (PARI)
%o A181819(n) = factorback(apply(e->prime(e),(factor(n)[,2])));
%o memoA354349 = Map();
%o A354349(n) = if(1==n,1,my(v); if(mapisdefined(memoA354349,n,&v), v, v = -sumdiv(n,d,if(d<n,A181819(n/d)*A354349(d),0)); mapput(memoA354349,n,v); (v)));
%Y Cf. A181819.
%Y Cf. also A354186, A354351, A354359.
%K sign,mult
%O 1,2
%A _Antti Karttunen_, Jun 05 2022