

A127707


Number of commutative rings with 1 containing n elements.


12



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
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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



