%I #27 Apr 19 2022 07:22:24

%S 1,1,1,4,1,1,1,10,4,1,1,4,1,1,1,37,1,4,1,4,1,1,1,10,4,1,11,4,1,1,1,

%T 109,1,1,1,16,1,1,1,10,1,1,1,4,4,1,1,37,4,4,1,4,1,11,1,10,1,1,1,4,1,1,

%U 4

%N Number of commutative rings with 1 containing n elements.

%C Is this a multiplicative function?

%C Answer: yes! See the Eric M. Rains link for a proof for the result for all unital rings; restricting to commutative rings does not affect the essence of the proof. - _Jianing Song_, Feb 02 2020

%H C. Noebauer, <a href="https://web.archive.org/web/20080111141811/http://www.algebra.uni-linz.ac.at/~noebsi/">Home page</a> and <a href="https://web.archive.org/web/20061002201537/http://www.algebra.uni-linz.ac.at/~noebsi/ringtable.html">Table of numbers of small rings</a> [Archived copies from web.archive.org]

%H Eric M. Rains, <a href="/A037291/a037291.txt">The number of unital rings with n elements is a multiplicative function of n.</a>

%F a(n) = A037291(n) - A127708(n). - _Bernard Schott_, Apr 19 2022

%Y Cf. A037289, A037291, A127708, A027623, A307000, A341202.

%K more,nice,nonn,mult

%O 1,4

%A Hugues Randriam (randriam(AT)enst.fr), Jan 24 2007

%E Keyword 'mult' added by _Jianing Song_, Feb 02 2020

%E a(32)-a(63) using Nöbauer's data added by _Andrey Zabolotskiy_, Apr 18 2022

%E a(32) = 109 corrected by _Bernard Schott_, Apr 19 2022