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 A387061 #15 Aug 25 2025 04:26:22
%S A387061 0,0,1,5,23,99,479,2645,19599,154007,1271519,11688489,126123095,
%T A387061 1481833859,15162417087,126294191309,2497347563039,53642575418415,
%U A387061 937621220224319,17116389710781136,281286727706878100
%N A387061 Number of Sylow permutations in S_n.
%C A387061 Sylow permutations are permutations for which the induced group is a Sylow group.
%C A387061 Equivalently, a permutation x is Sylow if there exists a prime number p, such that for each cycle c in the cycle decomposition of x, c has length some power of p.
%C A387061 Not all cycles need to have the same length; e.g., ((1 2)(3 4 5 6)) is a Sylow permutation in S_6.
%C A387061 We exclude the identity from Sylow permutations.
%C A387061 All permutation groups are uniquely characterized by the Sylow permutations they contain (and one can reconstruct said permutation group by computing the group induced by this set).
%e A387061 For a(3) = 5, the solutions are { ((1 2)) ((1 3)) ((2 3)) ((1 2 3)) ((1 3 2)) } (1-length cycles are omitted from the decomposition).
%e A387061 For a(4) = 23, the solutions are (up to permutation) { ((1 2)) ((1 2)(3 4)) ((1 2 3 4)) ((1 2 3)) }.
%e A387061 For a(6) = 479, the solutions include (for example) ((1 2)(3 4 5 6)) but not ((1 2)(3 4 5)).
%Y A387061 Cf. A000142, A186202.
%K A387061 nonn,more,new
%O A387061 0,4
%A A387061 _Joan Thibault_, Aug 15 2025