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A270492 a(n) = gcd(r) where r ranges over the orders of all subgroups whose direct product gives the multiplicative group modulo n.

%I A270492 #33 Mar 13 2018 04:11:11
%S A270492 0,0,2,2,4,2,6,2,6,4,10,2,12,6,2,2,16,6,18,2,2,10,22,2,20,12,18,2,28,
%T A270492 2,30,2,2,16,2,2,36,18,2,2,40,2,42,2,2,22,46,2,42,20,2,2,52,18,2,2,2,
%U A270492 28,58,2,60,30,6,2,4,2,66,2,2,2,70,2,72,36,2,2,2,2,78,2,54,40,82,2,4,42,2,2,88,2,6,2
%N A270492 a(n) = gcd(r) where r ranges over the orders of all subgroups whose direct product gives the multiplicative group modulo n.
%H A270492 Antti Karttunen, <a href="/A270492/b270492.txt">Table of n, a(n) for n = 1..10000</a>
%F A270492 a(p) = p - 1 for odd primes p.
%F A270492 a(p^k) = phi(p^k) = (p-1)*p^(k-1) for odd primes p and k >= 1.
%F A270492 a(n) = A052409(A289625(n)). - _Antti Karttunen_, Aug 07 2017
%o A270492 (PARI) a(n)=gcd(znstar(n)[2]);
%Y A270492 Cf. A002322 (LCM over the orders of all subgroups), A052409, A289625, A290084.
%K A270492 nonn
%O A270492 1,3
%A A270492 _Joerg Arndt_, Mar 18 2016
%E A270492 Terms a(1) and a(2) changed from 1 to 0 by _Antti Karttunen_, Aug 07 2017