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%I #115 Feb 26 2024 14:22:58
%S 1,1,2,3,8,10,36,41,132,250,700,750,4010,4237,10680,24679,87328,90478,
%T 435812,449586,1939684,3853278,8650900,8840110,60035322,80605209,
%U 177211024,368759752,1380348224,1401414640,8892787136,9014369784,33923638848,59455553072,126536289568,207587882368
%N Number of permutations sigma of {1,2,...,n} such that sigma(i) divides i or i divides sigma(i) for 1 <= i <= n.
%H Carl Pomerance, <a href="https://arxiv.org/abs/2203.03085">Coprime permutations</a>, arXiv:2203.03085 [math.NT], 2022.
%H Carl Pomerance, <a href="https://arxiv.org/abs/2206.01699">Permutations with arithmetic constraints</a>, arXiv:2206.01699 [math.NT], 2022.
%F a(n) = Permanent((x_{ij})) with x_{ij} = 1 if i divides j or j divides i and x_{ij} = 0 otherwise for i,j = 1,...,n. - _M. Farrokhi D. G._, Dec 30 2018
%e In case n = 4:
%e permutation
%e ------------
%e [1, 2, 3, 4]
%e [1, 4, 3, 2]
%e [2, 1, 3, 4]
%e [2, 4, 3, 1]
%e [3, 2, 1, 4]
%e [3, 4, 1, 2]
%e [4, 1, 3, 2]
%e [4, 2, 3, 1]
%t a[n_] := a[n] = If[n == 0, 1,Permanent[Table[If[Divisible[i, j] || Divisible[j, i], 1, 0], {i, n}, {j, n}]]];
%t Table[Print[n, " ", a[n]]; a[n], {n, 0, 22}] (* _Jean-François Alcover_, Jun 25 2022 *)
%o (PARI) a(n) = matpermanent(matrix(n, n, i, j, if (!(i%j) || !(j%i), 1, 0))); \\ _Michel Marcus_, Dec 30 2018
%Y Cf. A005326, A263987.
%K nonn
%O 0,3
%A _Seiichi Manyama_, Dec 18 2018
%E a(0), a(24)-a(30) from _Alois P. Heinz_, Dec 19 2018
%E a(31)-a(35) from _M. Farrokhi D. G._, Dec 30 2018
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