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%I #9 Jun 05 2022 23:20:28
%S 1,-2,-2,-2,-2,4,-2,-14,-2,4,-2,4,-2,4,4,-110,-2,4,-2,4,4,4,-2,28,-2,
%T 4,-14,4,-2,-8,-2,-1526,4,4,4,4,-2,4,4,28,-2,-8,-2,4,4,4,-2,220,-2,4,
%U 4,4,-2,28,4,28,4,4,-2,-8,-2,4,4,-20858,4,-8,-2,4,4,-8,-2,28,-2,4,4,4,4,-8,-2,220,-110,4,-2,-8
%N Dirichlet inverse of A124859.
%C Multiplicative because A124859 is.
%H Antti Karttunen, <a href="/A354359/b354359.txt">Table of n, a(n) for n = 1..20000</a>
%F a(1) = 1, and for n > 1, a(n) = -Sum_{d|n, d < n} A124859(n/d) * a(d).
%o (PARI)
%o A124859(n) = { my(f=factor(n)); for(k=1, #f~, f[k, 1] = prod(j=1, f[k, 2], prime(j)); f[k, 2] = 1); factorback(f); }; \\ From A124859
%o memoA354359 = Map();
%o A354359(n) = if(1==n,1,my(v); if(mapisdefined(memoA354359,n,&v), v, v = -sumdiv(n,d,if(d<n,A124859(n/d)*A354359(d),0)); mapput(memoA354359,n,v); (v)));
%Y Cf. A002110, A124859.
%Y Cf. also A354186, A354349, A354351, A354358.
%K sign,mult
%O 1,2
%A _Antti Karttunen_, Jun 05 2022
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