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A333082 Number of permutations sigma of [n] such that all values sigma(k)/k for 1 <= k <= n are pairwise distinct.

%I A333082 #19 Mar 09 2020 09:14:03
%S A333082 1,1,1,5,13,79,345,2785,19595,171141,1555181,18998391,184988197,
%T A333082 2675065491,35582840563,490186693669
%N A333082 Number of permutations sigma of [n] such that all values sigma(k)/k for 1 <= k <= n are pairwise distinct.
%H A333082 Wikipedia, <a href="https://en.wikipedia.org/wiki/Permutation">Permutation</a>
%t A333082 Table[ Count[ Length[ Union[ #/ Range[n]]] & /@ Permutations[ Range@n], n], {n, 0, 9}] (* _Giovanni Resta_, Mar 09 2020 *)
%o A333082 (Ruby)
%o A333082 def A(n)
%o A333082   (1..n).to_a.permutation.select{|i| (1..n).map{|j| i[j - 1] / j.to_r}.uniq.size == n}.size
%o A333082 end
%o A333082 def A333082(n)
%o A333082   (0..n).map{|i| A(i)}
%o A333082 end
%o A333082 p A333082(9)
%Y A333082 Cf. A333083.
%K A333082 nonn,more
%O A333082 0,4
%A A333082 _Seiichi Manyama_, Mar 07 2020
%E A333082 a(13)-a(15) from _Giovanni Resta_, Mar 09 2020