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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.
1
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
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
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Oct 01 2022
STATUS
approved