A127707 Number of commutative rings with 1 containing n elements.

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, 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, 4

Offset: 1

Author

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

Keywords

• more
• nice
• nonn
• mult

Comments

Is this a multiplicative function?

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

Links

• C. Noebauer, Home page and Table of numbers of small rings [Archived copies from web.archive.org]
• Eric M. Rains, The number of unital rings with n elements is a multiplicative function of n.

Crossrefs

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

Formula

a(n) = A037291(n) - A127708(n). - Bernard Schott, Apr 19 2022

Extensions

Keyword 'mult' added by Jianing Song, Feb 02 2020

a(32)-a(63) using Nöbauer's data added by Andrey Zabolotskiy, Apr 18 2022

a(32) = 109 corrected by Bernard Schott, Apr 19 2022