A361871 - OEIS

%I #15 Aug 11 2023 09:53:26

%S 6,6,6,8,10,12,14,16,18,20,22,24,26,28,30,32,34,36,38,40,42,44,46,48,

%T 50,52,54,56,58,60,62,64,66,68,70,72,74,76,78,80,82,84,86,88,90,92,94,

%U 96,98,100,102,104,106,108,110,112,114,116,118,120

%N The smallest order of a non-abelian group with an element of order n.

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Lagrange%27s_theorem_(group_theory)">Lagrange's theorem (group theory)</a>

%F a(n) = 2*n for n >= 3.

%F Proof: By Lagrange's theorem in group theory we have that n divides a(n) for all n. A group of order n and with an element of order n is the cyclic group of order n, hence being abelian. On the other hand, the dihedral group D_{2n} is non-abelian for n >= 3 and contains an element of order n. - _Jianing Song_, Aug 11 2023

%Y Essentially the same as A163300, A103517, A051755.

%K nonn,easy

%O 1,1

%A _Yue Yu_, Apr 01 2023