A034381 Number of labeled cyclic groups with n elements.

1, 2, 3, 12, 30, 360, 840, 10080, 60480, 907200, 3991680, 119750400, 518918400, 14529715200, 163459296000, 2615348736000, 22230464256000, 1067062284288000, 6758061133824000, 304112751022080000, 4257578514309120000, 112400072777760768000, 1175091669949317120000

Offset: 1

Author

Christian G. Bower

Keywords

• nonn
• easy

Comments

This sequence is strictly increasing, since a(n) = n!/phi(n) > n!/n = (n-1)! >= a(n-1) for n >= 2. - Jianing Song, Mar 02 2024

Links

• Jianing Song, Table of n, a(n) for n = 1..450
• Index entries for sequences related to groups

Crossrefs

Cf. A000010, A000142, A034382, A034383, A058161.

Programs

PARI

a(n) = n! / eulerphi(n) \\ Jianing Song, Mar 02 2024

Formula

a(n) = n!/phi(n).

a(n) = A000142(n)/A000010(n) = n*A058161(n).

Extensions

a(21) onwards from Jianing Song, Mar 02 2024