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%I #17 Apr 02 2022 09:31:13
%S 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,
%T 1
%N Number of rings without 1 containing n elements.
%C 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).
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Pseudo-ring">Pseudo-ring</a>.
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Rng_(algebra)">Rng</a>.
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Zero_ring">Zero ring</a>.
%H <a href="/index/Res#rings">Index to sequences related to rings</a>.
%F a(n) = A037234(n) - A037291(n) = A342375(n) + A342376(n).
%F a(p) = 1 if p prime.
%e 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.
%e a(3) = 1 because the Matrix ring with 3 elements with coefficients from Z/3Z:
%e (0 0) (0 0) (0 0)
%e 0 = (0 0), a = (1 0), b = (2 0)
%e 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.
%Y Number of rings: A037291 (with 1 containing n elements), this sequence (without 1 containing n elements), A027623 or A037234 (with n elements).
%Y Cf. A127707, A342375, A037289, A127708, A342376, A209401.
%K nonn,more
%O 1,4
%A _Bernard Schott_, Mar 12 2021
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