This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A342377 #17 Apr 02 2022 09:31:13 %S A342377 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 A342377 1 %N A342377 Number of rings without 1 containing n elements. %C A342377 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 A342377 Wikipedia, <a href="https://en.wikipedia.org/wiki/Pseudo-ring">Pseudo-ring</a>. %H A342377 Wikipedia, <a href="https://en.wikipedia.org/wiki/Rng_(algebra)">Rng</a>. %H A342377 Wikipedia, <a href="https://en.wikipedia.org/wiki/Zero_ring">Zero ring</a>. %H A342377 <a href="/index/Res#rings">Index to sequences related to rings</a>. %F A342377 a(n) = A037234(n) - A037291(n) = A342375(n) + A342376(n). %F A342377 a(p) = 1 if p prime. %e A342377 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 A342377 a(3) = 1 because the Matrix ring with 3 elements with coefficients from Z/3Z: %e A342377 (0 0) (0 0) (0 0) %e A342377 0 = (0 0), a = (1 0), b = (2 0) %e A342377 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 A342377 Number of rings: A037291 (with 1 containing n elements), this sequence (without 1 containing n elements), A027623 or A037234 (with n elements). %Y A342377 Cf. A127707, A342375, A037289, A127708, A342376, A209401. %K A342377 nonn,more %O A342377 1,4 %A A342377 _Bernard Schott_, Mar 12 2021