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

1,4

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

Table of n, a(n) for n=1..63.

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.

Formula

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

Crossrefs

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

Sequence in context: A303278 A222639 A184729 * A113196 A037291 A222317

Adjacent sequences: A127704 A127705 A127706 * A127708 A127709 A127710

Keyword

more,nice,nonn,mult

Author

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

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

Status

approved