

A178254


Number of permutations of the proper divisors of n such that no adjacent elements have a common divisor greater than 1.


8



1, 1, 1, 2, 1, 6, 1, 2, 2, 6, 1, 4, 1, 6, 6, 0, 1, 4, 1, 4, 6, 6, 1, 0, 2, 6, 2, 4, 1, 36, 1, 0, 6, 6, 6, 0, 1, 6, 6, 0, 1, 36, 1, 4, 4, 6, 1, 0, 2, 4, 6, 4, 1, 0, 6, 0, 6, 6, 1, 0, 1, 6, 4, 0, 6, 36, 1, 4, 6, 36, 1, 0, 1, 6, 4, 4, 6, 36, 1, 0, 0, 6, 1, 0, 6, 6, 6, 0, 1, 0, 6, 4, 6, 6, 6, 0, 1, 4, 4, 0, 1, 36, 1
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OFFSET

1,4


COMMENTS

Depends only on prime signature;
range = {0, 1, 2, 4, 6, 36};
a(A033987(n)) = 0; a(A037144(n)) > 0;
a(A008578(n))=1; a(A168363(n))=2; a(A054753(n))=4; a(A006881(n))=6; a(A007304(n))=36.


LINKS

R. Zumkeller, Table of n, a(n) for n = 1..10000
R. Zumkeller, Example: n=42


EXAMPLE

Proper divisors for n=21 are: 1, 3, and 7:
a(39) = #{[1,3,7], [1,7,3], [3,1,7], [3,7,1], [7,1,3], [7,3,1]} = 6;
proper divisors for n=12 are: 1, 2, 3, 4, and 6:
a(12) = #{[2,3,4,1,6], [4,3,2,1,6], [6,1,2,3,4], [6,1,4,3,2]} = 4;
proper divisors for n=42: 1, 2, 3, 6, 7, 14, and 21:
a(42) = #{[2,21,1,6,7,3,14], [2,21,1,14,3,7,6], [3,14,1,6,7,2,21], [3,14,1,21,2,7,6], [6,1,14,3,7,2,21], [6,1,21,2,7,3,14], ...} = 36, see the appended file for the list of all permutations.


CROSSREFS

Cf. A109810.
Sequence in context: A229818 A324500 A082388 * A085099 A193807 A225766
Adjacent sequences: A178251 A178252 A178253 * A178255 A178256 A178257


KEYWORD

nonn


AUTHOR

Reinhard Zumkeller, May 24 2010


STATUS

approved



