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

1,3

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.

Links

Table of n, a(n) for n=1..87.

Example

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

Prog

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

Crossrefs

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

Sequence in context: A069922 A072211 A360825 * A299020 A343505 A365687

Adjacent sequences: A328922 A328923 A328924 * A328926 A328927 A328928

Keyword

nonn

Author

Jianing Song, Oct 31 2019

Status

approved