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A340187 Dirichlet inverse of A063994(x) = Product_{primes p dividing x} gcd(p-1, x-1).

%I A340187 #9 Dec 31 2020 15:34:45
%S A340187 1,-1,-2,0,-4,3,-6,0,2,7,-10,-1,-12,11,12,0,-16,-5,-18,-3,20,19,-22,0,
%T A340187 12,23,-2,-7,-28,-29,-30,0,36,31,44,4,-36,35,44,0,-40,-49,-42,-9,-24,
%U A340187 43,-46,0,30,-33,60,-13,-52,7,76,4,68,55,-58,23,-60,59,-36,0,80,-93,-66,-15,84,-119,-70,-1,-72,71,-52,-19
%N A340187 Dirichlet inverse of A063994(x) = Product_{primes p dividing x} gcd(p-1, x-1).
%H A340187 Antti Karttunen, <a href="/A340187/b340187.txt">Table of n, a(n) for n = 1..10000</a>
%H A340187 Antti Karttunen, <a href="/A340187/a340187.txt">Data supplement: n, a(n) computed for n = 1..65537</a>
%o A340187 (PARI)
%o A340187 up_to = 65537;
%o A340187 A063994(n) = { my(f=factor(n)); prod(i=1, #f~, gcd(f[i, 1]-1, n-1)); };
%o A340187 DirInverse(v) = { my(u=vector(#v)); u[1] = (1/v[1]); for(n=2, #v, u[n] = -sumdiv(n, d, if(d<n, v[n/d]*u[d], 0))); (u) }; \\ Compute the Dirichlet inverse of the sequence given in input vector v.
%o A340187 v340187 = DirInverse(vector(up_to, n, A063994(n)));
%o A340187 A340187(n) = v340187[n];
%Y A340187 Cf. A063994, A340188, A340189.
%Y A340187 Cf. also A023900, A340142, A340145, A340190.
%K A340187 sign
%O A340187 1,3
%A A340187 _Antti Karttunen_, Dec 31 2020