A178254 Number of permutations of the proper divisors of n such that no adjacent elements have a common divisor greater than 1.

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

Offset: 1

Author

Reinhard Zumkeller, May 24 2010

Keywords

• nonn

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.

Examples

			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.
		

Links

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

Crossrefs

Cf. A109810.