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A357328 Number of permutations p of [n] such that p(i) divides p(j) if i divides j for 1 <= i <= j <= n.

%I A357328 #42 Oct 02 2022 10:30:09
%S A357328 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 A357328 48,48,240,240,120,48,48,48,240,144,96,96,480,480,2880,1440,1440,720,
%U A357328 4320,4320,4320,4320,2880,2880,20160,20160,10080,10080,10080,2880,20160,20160,161280,60480,60480,60480,120960
%N A357328 Number of permutations p of [n] such that p(i) divides p(j) if i divides j for 1 <= i <= j <= n.
%C A357328 a(n) >= 1.
%H A357328 Seiichi Manyama, <a href="/A357328/b357328.txt">Table of n, a(n) for n = 0..5000</a>
%e A357328 For n = 14, the 4 permutations are:
%e A357328   [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14]
%e A357328   [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 13, 12, 11, 14]
%e A357328   [1, 2, 3, 4, 7, 6, 5, 8, 9, 14, 11, 12, 13, 10]
%e A357328   [1, 2, 3, 4, 7, 6, 5, 8, 9, 14, 13, 12, 11, 10]
%o A357328 (Ruby)
%o A357328 require 'prime'
%o A357328 def f(n)
%o A357328   return 1 if n < 2
%o A357328   (1..n).inject(:*)
%o A357328 end
%o A357328 def A(n)
%o A357328   h = {}
%o A357328   Prime.each(n).each{|i|
%o A357328     h[i] = n / i
%o A357328   }
%o A357328   h.group_by{|k, v| v}.inject(1){|s, i| s * f(i.last.size)}
%o A357328 end
%o A357328 def A357328(n)
%o A357328   (0..n).map{|i| A(i)}
%o A357328 end
%o A357328 p A357328(100)
%Y A357328 Cf. A320843.
%K A357328 nonn
%O A357328 0,4
%A A357328 _Seiichi Manyama_, Oct 01 2022