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 A368943 #24 Jan 12 2024 10:05:15 %S A368943 1,1,1,1,3,7,11,23,50 %N A368943 Number of unlabeled mappings from n points to themselves with unique square root (endofunctions). %C A368943 A mapping f has a unique square root if there exists a unique g such that gg = f. %C A368943 Two mappings (endofunctions) are taken to be equivalent up to labeling if one is the conjugation of the other by a permutation. (Conjugation is applying the inverse permutation, the endofunction, and then the permutation, in that order. This is equivalent to permuting the "labels" of the set.) %H A368943 Keith J. Bauer, <a href="/A368943/a368943.png">Visualization of a(6)</a> %e A368943 For n = 4, representatives of the a(4) = 3 mappings up to relabeling are %e A368943 1->1 2->1 3->2 4->1 %e A368943 1->2 2->3 3->1 4->1 %e A368943 1->2 2->3 3->1 4->4 %e A368943 whose unique square roots are respectively %e A368943 1->1 2->1 3->4 4->2 %e A368943 1->3 2->1 3->2 4->2 %e A368943 1->3 2->1 3->2 4->4 %Y A368943 The labeled version is A368867. %Y A368943 Cf. A000700 (permutations only) < this sequence < A368830 (any square maps) < A001372 (all maps). %K A368943 nonn,hard,more %O A368943 0,5 %A A368943 _Keith J. Bauer_, Jan 11 2024 %E A368943 a(8) from _Andrew Howroyd_, Jan 10 2024