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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. 2
1, 1, 1, 3, 13, 67, 305, 2359, 16495, 141643, 1273691, 15580299, 152788607, 2206382433, 28916044241, 399450183613 (list; graph; refs; listen; history; text; internal format)
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: A142979 A302303 A201713 * 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

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Last modified March 4 02:14 EST 2021. Contains 341773 sequences. (Running on oeis4.)