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A323406 Greatest common divisor of Product (p_i^e_i)-1 and Product (p_i^e_i)+1, when n = Product (p_i^e_i): a(n) = gcd(A047994(n), A034448(n)).

%I A323406 #9 Jan 15 2019 18:43:07
%S A323406 1,1,2,1,2,2,2,1,2,2,2,2,2,6,8,1,2,2,2,6,4,2,2,2,2,6,2,2,2,8,2,1,4,2,
%T A323406 24,2,2,6,8,2,2,12,2,30,4,2,2,2,2,6,8,2,2,2,8,6,4,2,2,24,2,6,16,1,12,
%U A323406 4,2,6,4,24,2,2,2,6,8,2,12,24,2,6,2,2,2,4,4,6,8,2,2,4,8,6,4,2,24,2,2,6,40,2,2,8,2,42,48
%N A323406 Greatest common divisor of Product (p_i^e_i)-1 and Product (p_i^e_i)+1, when n = Product (p_i^e_i): a(n) = gcd(A047994(n), A034448(n)).
%H A323406 Antti Karttunen, <a href="/A323406/b323406.txt">Table of n, a(n) for n = 1..20000</a>
%H A323406 Antti Karttunen, <a href="/A323406/a323406.txt">Data supplement: n, a(n) computed for n = 1..100000</a>
%F A323406 a(n) = gcd(A034448(n), A047994(n)), where A034448 is unitary sigma, and A047994 is unitary phi.
%o A323406 (PARI)
%o A323406 A047994(n) = { my(f=factor(n)~); prod(i=1, #f, f[1, i]^f[2, i]-1); };
%o A323406 A034448(n) = { my(f=factor(n)); prod(k=1, #f~, 1+(f[k, 1]^f[k, 2])); }; \\ After code in A034448
%o A323406 A323406(n) = gcd(A034448(n), A047994(n));
%Y A323406 Cf. A034448, A047994.
%Y A323406 Cf. also A009223, A066086, A126865, A322362, A323166, A323409.
%K A323406 nonn
%O A323406 1,3
%A A323406 _Antti Karttunen_, Jan 15 2019