|
| |
|
|
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
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
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
|
| |
|
|
