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

1, 1, 1, 3, 13, 67, 305, 2359, 16495, 141643, 1273691, 15580299, 152788607, 2206382433, 28916044241, 399450183613

Offset

0,4

Links

Table of n, a(n) for n=0..15.

Wikipedia, Permutation

Example

In the n=3 case:
    | sigma(1),sigma(2),sigma(3)
----+---------------------------
  1 | [1, 2, 3]
  2 | [2, 3, 1]
  3 | [3, 1, 2]

Mathematica

Table[ Count[ Length@ Union[# Range@ n] & /@ Permutations@ Range@ n, n], {n, 0, 9}] (* Giovanni Resta, Mar 09 2020 *)

Prog

(Ruby)
def A(n)
  (1..n).to_a.permutation.select{|i| (1..n).map{|j| i[j - 1] * j}.uniq.size == n}.size
end
def A333083(n)
  (0..n).map{|i| A(i)}
end
p A333083(9)
(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

Crossrefs

Cf. A333082.

Sequence in context: A302303 A201713 A343204 * A298611 A136784 A284717

Adjacent sequences: A333080 A333081 A333082 * A333084 A333085 A333086

Keyword

nonn,more

Author

Seiichi Manyama, Mar 07 2020

Extensions

a(13)-a(15) from Giovanni Resta, Mar 09 2020

Status

approved