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 A383458 #7 May 27 2025 19:21:43 %S A383458 1,1,1,1,2,3,2,2,2,3,4,3,4,3,3,3,4,5,4,5,6,7,4,5,4 %N A383458 Maximum number of cycles in any permutation in S_n of the highest order (A000793(n)). %C A383458 Landau's function g(n) = A000793(n) gives the maximum order of any permutation on n elements. %C A383458 The number of permutations of order g(n) is A074059, and the number of different cycle types of permutations of order g(n) is A074064. a(n) is the maximum number of cycles in any permutation of order g(n), and A383459(n) is the minimum number of cycles in any permutation of order g(n). %e A383458 There are two different cycle types of permutations in S_6 of the maximum order g(6) = 6, for example (123456) and (12)(345)(6). The minimum number of cycles is A383459(6) = 1 and maximum number is a(6) = 3. %o A383458 (Julia) %o A383458 using Combinatorics %o A383458 arrs = [] %o A383458 for n in 1:25 %o A383458 ps = integer_partitions(n) %o A383458 lcms = lcm.(ps) %o A383458 the_max, imax, = findmax(lcms) %o A383458 max_order_cyc_idxs = [] %o A383458 for (i, l) in enumerate(lcms) %o A383458 if the_max == l %o A383458 push!(max_order_cyc_idxs, i) %o A383458 end %o A383458 end %o A383458 push!(arrs, ps[max_order_cyc_idxs]) %o A383458 end %o A383458 map(x->maximum(length.(x)), arrs) %Y A383458 Cf. A000793, A074059, A074064, A383459. %K A383458 nonn,more %O A383458 1,5 %A A383458 _Anand Jain_, Mar 22 2025