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A333083 Number of permutations sigma of [n] such that all values k * sigma(k) for 1 <= k <= n are pairwise distinct.

%I A333083 #28 Mar 09 2020 13:01:50
%S A333083 1,1,1,3,13,67,305,2359,16495,141643,1273691,15580299,152788607,
%T A333083 2206382433,28916044241,399450183613
%N A333083 Number of permutations sigma of [n] such that all values k * sigma(k) for 1 <= k <= n are pairwise distinct.
%H A333083 Wikipedia, <a href="https://en.wikipedia.org/wiki/Permutation">Permutation</a>
%e A333083 In the n=3 case:
%e A333083     | sigma(1),sigma(2),sigma(3)
%e A333083 ----+---------------------------
%e A333083   1 | [1, 2, 3]
%e A333083   2 | [2, 3, 1]
%e A333083   3 | [3, 1, 2]
%t A333083 Table[ Count[ Length@ Union[# Range@ n] & /@ Permutations@ Range@ n, n], {n, 0, 9}] (* _Giovanni Resta_, Mar 09 2020 *)
%o A333083 (Ruby)
%o A333083 def A(n)
%o A333083   (1..n).to_a.permutation.select{|i| (1..n).map{|j| i[j - 1] * j}.uniq.size == n}.size
%o A333083 end
%o A333083 def A333083(n)
%o A333083   (0..n).map{|i| A(i)}
%o A333083 end
%o A333083 p A333083(9)
%o A333083 (PARI) a(n) = {my(nb=0); forperm([1..n], p, if (#Set(vector(n, k, k*p[k])) == n, nb++);); nb;} \\ _Michel Marcus_, Mar 09 2020
%Y A333083 Cf. A333082.
%K A333083 nonn,more
%O A333083 0,4
%A A333083 _Seiichi Manyama_, Mar 07 2020
%E A333083 a(13)-a(15) from _Giovanni Resta_, Mar 09 2020