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

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, 48, 48, 240, 240, 120, 48, 48, 48, 240, 144, 96, 96, 480, 480, 2880, 1440, 1440, 720, 4320, 4320, 4320, 4320, 2880, 2880, 20160, 20160, 10080, 10080, 10080, 2880, 20160, 20160, 161280, 60480, 60480, 60480, 120960

Offset

0,4

Comments

a(n) >= 1.

Links

Seiichi Manyama, Table of n, a(n) for n = 0..5000

Example

For n = 14, the 4 permutations are:
  [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14]
  [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 13, 12, 11, 14]
  [1, 2, 3, 4, 7, 6, 5, 8, 9, 14, 11, 12, 13, 10]
  [1, 2, 3, 4, 7, 6, 5, 8, 9, 14, 13, 12, 11, 10]

Prog

(Ruby)
require 'prime'
def f(n)
  return 1 if n < 2
  (1..n).inject(:*)
end
def A(n)
  h = {}
  Prime.each(n).each{|i|
    h[i] = n / i
  }
  h.group_by{|k, v| v}.inject(1){|s, i| s * f(i.last.size)}
end
def A357328(n)
  (0..n).map{|i| A(i)}
end
p A357328(100)

Crossrefs

Cf. A320843.

Sequence in context: A317994 A128428 A056171 * A333749 A238949 A076755

Adjacent sequences: A357325 A357326 A357327 * A357329 A357330 A357331

Keyword

nonn

Author

Seiichi Manyama, Oct 01 2022

Status

approved