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

1,3

Links

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

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

Prog

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

Crossrefs

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

Sequence in context: A140635 A283465 A283466 * A002322 A127835 A117004

Adjacent sequences: A270489 A270490 A270491 * A270493 A270494 A270495

Keyword

nonn

Author

Joerg Arndt, Mar 18 2016

Extensions

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

Status

approved