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A342377 Number of rings without 1 containing n elements. 3
0, 1, 1, 7, 1, 3, 1, 41, 7, 3, 1, 18, 1, 3, 3, 340, 1, 18, 1, 18, 3, 3, 1, 93, 7, 3, 47, 18, 1, 7, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,4
COMMENTS
A ring without 1 is still a ring, although sometimes called a rng, or a non-unital ring, or a pseudo-ring (see Wikipedia links).
LINKS
Wikipedia, Pseudo-ring.
Wikipedia, Rng.
Wikipedia, Zero ring.
FORMULA
a(n) = A037234(n) - A037291(n) = A342375(n) + A342376(n).
a(p) = 1 if p prime.
EXAMPLE
a(1) = 0 because the only ring with 1 element is the zero ring (see link) with the element 0, and for this ring, 0 and 1 coincide.
a(3) = 1 because the Matrix ring with 3 elements with coefficients from Z/3Z:
(0 0) (0 0) (0 0)
0 = (0 0), a = (1 0), b = (2 0)
is without 1 (note this ring is commutative) and there is no other such ring with 3 elements and without 1, hence a(3) = 1.
CROSSREFS
Number of rings: A037291 (with 1 containing n elements), this sequence (without 1 containing n elements), A027623 or A037234 (with n elements).
Sequence in context: A317834 A340144 A340141 * A346103 A039616 A344967
KEYWORD
nonn,more
AUTHOR
Bernard Schott, Mar 12 2021
STATUS
approved

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Last modified March 28 05:39 EDT 2024. Contains 371235 sequences. (Running on oeis4.)