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A340190 Möbius transform of A063994(x) = Product_{primes p dividing x} gcd(p-1, x-1).

%I A340190 #9 Dec 31 2020 15:35:06
%S A340190 1,0,1,0,3,-1,5,0,0,-3,9,0,11,-5,-1,0,15,0,17,0,-3,-9,21,0,0,-11,0,2,
%T A340190 27,1,29,0,-7,-15,-5,0,35,-17,-9,0,39,3,41,0,4,-21,45,0,0,0,-13,2,51,
%U A340190 0,-9,-2,-15,-27,57,0,59,-29,0,0,1,11,65,0,-19,7,69,0,71,-35,0,2,-11,9,77,0,0,-39,81,-2,-3,-41,-25
%N A340190 Möbius transform of A063994(x) = Product_{primes p dividing x} gcd(p-1, x-1).
%H A340190 Antti Karttunen, <a href="/A340190/b340190.txt">Table of n, a(n) for n = 1..8191</a>
%H A340190 Antti Karttunen, <a href="/A340190/a340190.txt">Data supplement: n, a(n) computed for n = 1..65537</a>
%F A340190 a(n) = Sum_{d|n} A008683(n/d) * A063994(d).
%F A340190 a(n) = A063994(n) - A340191(n).
%o A340190 (PARI)
%o A340190 A063994(n) = { my(f=factor(n)); prod(i=1, #f~, gcd(f[i, 1]-1, n-1)); };
%o A340190 A340190(n) = sumdiv(n,d,moebius(n/d)*A063994(d));
%Y A340190 Cf. A008683, A063994, A340191.
%Y A340190 Cf. also A007431, A340143, A340146, A340192.
%K A340190 sign
%O A340190 1,5
%A A340190 _Antti Karttunen_, Dec 31 2020