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%I #42 Oct 02 2022 10:30:09
%S 1,1,1,2,1,2,1,2,2,2,1,2,2,6,4,2,2,6,6,24,24,24,6,24,24,24,12,12,12,
%T 48,48,240,240,120,48,48,48,240,144,96,96,480,480,2880,1440,1440,720,
%U 4320,4320,4320,4320,2880,2880,20160,20160,10080,10080,10080,2880,20160,20160,161280,60480,60480,60480,120960
%N Number of permutations p of [n] such that p(i) divides p(j) if i divides j for 1 <= i <= j <= n.
%C a(n) >= 1.
%H Seiichi Manyama, <a href="/A357328/b357328.txt">Table of n, a(n) for n = 0..5000</a>
%e For n = 14, the 4 permutations are:
%e [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14]
%e [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 13, 12, 11, 14]
%e [1, 2, 3, 4, 7, 6, 5, 8, 9, 14, 11, 12, 13, 10]
%e [1, 2, 3, 4, 7, 6, 5, 8, 9, 14, 13, 12, 11, 10]
%o (Ruby)
%o require 'prime'
%o def f(n)
%o return 1 if n < 2
%o (1..n).inject(:*)
%o end
%o def A(n)
%o h = {}
%o Prime.each(n).each{|i|
%o h[i] = n / i
%o }
%o h.group_by{|k, v| v}.inject(1){|s, i| s * f(i.last.size)}
%o end
%o def A357328(n)
%o (0..n).map{|i| A(i)}
%o end
%o p A357328(100)
%Y Cf. A320843.
%K nonn
%O 0,4
%A _Seiichi Manyama_, Oct 01 2022
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