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A340192 a(n) = Sum_{d|n} A063994(d), where A063994(x) = Product_{primes p dividing x} gcd(p-1, x-1).

%I A340192 #8 Dec 31 2020 15:35:32
%S A340192 1,2,3,3,5,5,7,4,5,7,11,7,13,9,11,5,17,8,19,9,13,13,23,9,9,15,7,13,29,
%T A340192 15,31,6,17,19,15,11,37,21,19,11,41,17,43,15,21,25,47,11,13,12,23,19,
%U A340192 53,11,19,15,25,31,59,19,61,33,19,7,33,25,67,21,29,21,71,14,73,39,19,25,21,23,79,13,9,43,83,23,37
%N A340192 a(n) = Sum_{d|n} A063994(d), where A063994(x) = Product_{primes p dividing x} gcd(p-1, x-1).
%H A340192 Antti Karttunen, <a href="/A340192/b340192.txt">Table of n, a(n) for n = 1..8191</a>
%H A340192 Antti Karttunen, <a href="/A340192/a340192.txt">Data supplement: n, a(n) computed for n = 1..65537</a>
%F A340192 a(n) = Sum_{d|n} A063994(d).
%F A340192 a(n) = n - A340193(n).
%o A340192 (PARI)
%o A340192 A063994(n) = { my(f=factor(n)); prod(i=1, #f~, gcd(f[i, 1]-1, n-1)); };
%o A340192 A340192(n) = sumdiv(n,d,A063994(d));
%Y A340192 Inverse Möbius transform of A063994.
%Y A340192 Cf. A340190, A340193.
%K A340192 nonn
%O A340192 1,2
%A A340192 _Antti Karttunen_, Dec 31 2020