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

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, 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, 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

Offset: 1

Author

Joerg Arndt, Mar 18 2016

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A002322 (LCM over the orders of all subgroups), A052409, A289625, A290084.

Programs

PARI

a(n)=gcd(znstar(n)[2]);

Formula

a(p) = p - 1 for odd primes p.

a(p^k) = phi(p^k) = (p-1)*p^(k-1) for odd primes p and k >= 1.

a(n) = A052409(A289625(n)). - Antti Karttunen, Aug 07 2017

Extensions

Terms a(1) and a(2) changed from 1 to 0 by Antti Karttunen, Aug 07 2017