A034381 - OEIS

%I #20 Mar 03 2024 17:17:01

%S 1,2,3,12,30,360,840,10080,60480,907200,3991680,119750400,518918400,

%T 14529715200,163459296000,2615348736000,22230464256000,

%U 1067062284288000,6758061133824000,304112751022080000,4257578514309120000,112400072777760768000,1175091669949317120000

%N Number of labeled cyclic groups with n elements.

%C 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

%H Jianing Song, <a href="/A034381/b034381.txt">Table of n, a(n) for n = 1..450</a>

%H <a href="/index/Gre#groups">Index entries for sequences related to groups</a>

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

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

%o (PARI) a(n) = n! / eulerphi(n) \\ _Jianing Song_, Mar 02 2024

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

%K nonn,easy

%O 1,2

%A _Christian G. Bower_

%E a(21) onwards from _Jianing Song_, Mar 02 2024