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%I #10 Jan 15 2019 18:43:28
%S 1,1,1,1,1,2,1,1,1,2,1,6,1,2,1,1,1,2,1,4,3,2,1,2,1,2,1,2,1,2,1,1,1,2,
%T 1,12,1,2,3,4,1,6,1,2,1,2,1,6,1,2,1,4,1,2,5,14,3,2,1,12,1,2,3,1,1,2,1,
%U 4,1,2,1,8,1,2,3,2,1,6,1,20,1,2,1,12,1,2,1,2,1,2,1,2,3,2,1,2,1,2,1,4,1,2,1,4,3
%N Greatest common divisor of Product (p_i^e_i)-1 and n, when n = Product (p_i^e_i); a(n) = gcd(n, A047994(n)).
%C Records 1, 2, 6, 12, 14, 20, 24, 84, 120, 168, 240, 468, 720, 1008, 1240, 1488, 1632, 7440, 9360, 14880, 32640, ... occur at n = 1, 6, 12, 36, 56, 80, 144, 168, 240, 504, 720, 1404, 3600, 4032, 4960, 8928, 13056, 14880, 28080, 44640, 65280, ...
%H Antti Karttunen, <a href="/A323409/b323409.txt">Table of n, a(n) for n = 1..16384</a>
%H Antti Karttunen, <a href="/A323409/a323409.txt">Data supplement: n, a(n) computed for n = 1..100000</a>
%F a(n) = gcd(n, A047994(n)), where A047994 is unitary phi.
%o (PARI)
%o A047994(n) = { my(f=factor(n)~); prod(i=1, #f, f[1, i]^f[2, i]-1); };
%o A323409(n) = gcd(n, A047994(n));
%Y Cf. A047994, A323410.
%Y Cf. also A009195, A323166, A323406.
%K nonn
%O 1,6
%A _Antti Karttunen_, Jan 15 2019
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