A328925 a(n) = A002322(n)/A118106(n); write n = Product_{i=1..t} p_i^e_i, then a(n) = A002322(n)/(lcm_{1<=i,j<=t,i!=j} ord(p_i,p_j^e_j)), where ord(a,r) is the multiplicative order of a modulo r, and A002322 is the Carmichael lambda (usually written as psi).

1, 1, 2, 2, 4, 1, 6, 2, 6, 1, 10, 1, 12, 2, 1, 4, 16, 1, 18, 1, 1, 1, 22, 1, 20, 1, 18, 1, 28, 1, 30, 8, 1, 2, 1, 1, 36, 1, 4, 1, 40, 1, 42, 1, 1, 2, 46, 1, 42, 1, 1, 1, 52, 1, 4, 1, 1, 1, 58, 1, 60, 6, 1, 16, 3, 1, 66, 2, 1, 1, 70, 1, 72, 1, 1, 1, 1, 1, 78, 1, 54, 2, 82, 1, 1, 3, 1

Offset: 1

Author

Jianing Song, Oct 31 2019

Keywords

• nonn

Comments

It is easy to see that A118106(n) divides psi(n) = A002322(n).

If n = p^e for prime p, then A118106(p^e) = 1, so a(p^e) = A002322(p^e). The other n's such that a(n) > 1 are listed in A329062.

Examples

			A002322(14) = 6, while A118106(14) = 3, so a(14) = 2.
		

Crossrefs

Cf. A002322, A118106, A328926 (indices of 1), A329062.

Programs

PARI

a(n) = A002322(n)/A118106(n) \\ See A002322 and A118106 for their programs