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%I #13 Jun 08 2022 15:48:47
%S 1,-1,-1,0,-1,-3,-1,-2,-5,1,-1,8,-1,-1,0,4,-1,18,-1,-2,-8,1,-1,0,-9,
%T -13,8,4,-1,9,-1,-2,-12,1,-4,-9,-1,-19,0,8,-1,29,-1,-2,10,-23,-1,2,
%U -13,4,-8,22,-1,20,0,2,0,1,-1,-13,-1,-1,26,2,-16,33,-1,-2,0,13,-1,-14,-1,-1,16,36,-16,37,-1,-10,19,1
%N Dirichlet inverse of function f(1) = 1, f(n) = gcd(A003415(n), A276086(n)) for n > 1.
%H Antti Karttunen, <a href="/A354348/b354348.txt">Table of n, a(n) for n = 1..30030</a>
%F a(1) = 1, and for n > 1, a(n) = -Sum_{d|n, d<n} A327858(n/d) * a(d).
%o (PARI)
%o A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
%o A276086(n) = { my(m=1, p=2); while(n, m *= (p^(n%p)); n = n\p; p = nextprime(1+p)); (m); };
%o A327858(n) = gcd(A003415(n), A276086(n));
%o memoA354348 = Map();
%o A354348(n) = if(1==n,1,my(v); if(mapisdefined(memoA354348,n,&v), v, v = -sumdiv(n,d,if(d<n,A327858(n/d)*A354348(d),0)); mapput(memoA354348,n,v); (v)));
%Y Cf. A003415, A276086, A327858.
%Y Cf. also A346242, A354347.
%K sign
%O 1,6
%A _Antti Karttunen_, Jun 08 2022
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