A037291 Number of rings with 1 containing n elements.

1, 1, 1, 4, 1, 1, 1, 11, 4, 1, 1, 4, 1, 1, 1, 50, 1, 4, 1, 4, 1, 1, 1, 11, 4, 1, 12, 4, 1, 1, 1, 208, 1, 1, 1, 16, 1, 1, 1, 11, 1, 1, 1, 4, 4, 1, 1, 50, 4, 4, 1, 4, 1, 12, 1, 11, 1, 1, 1, 4, 1, 1, 4

Offset

1,4

Comments

Many authors simply call these "rings". They are also known as unital rings, rings with unity, or rings with identity. - Charles R Greathouse IV, Aug 12 2015

Is this sequence multiplicative? That is, if p and q are distinct primes, is it true that a(p^i*q^j) = a(p^i)*a(q^j)? - Jianing Song, Oct 26 2019. The answer is yes - see the Eric M. Rains link. - N. J. A. Sloane, Oct 27 2019

Links

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

Gérard P. Michon, Ring Theory, Numericana, 2000-2022.

C. Noebauer, Home page and Table of numbers of small rings [Archived copies]

Eric M. Rains, The number of unital rings with n elements is a multiplicative function of n.

Crossrefs

Cf. A027623, A037221, A127707.

Sequence in context: A184729 A127707 A113196 * A222317 A063851 A124777

Adjacent sequences: A037288 A037289 A037290 * A037292 A037293 A037294

Keyword

nonn,nice,hard,mult

Author

Christian G. Bower, Jun 15 1998

Extensions

a(16) and a(32)-a(63) from Christof Noebauer (christof.noebauer(AT)algebra.uni-linz.ac.at), Sep 29 2000

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

a(54) corrected by Andrey Zabolotskiy, Feb 02 2023

Status

approved