A109810 Number of permutations of the positive divisors of n, where every element is coprime to its adjacent elements.

1, 2, 2, 2, 2, 4, 2, 0, 2, 4, 2, 0, 2, 4, 4, 0, 2, 0, 2, 0, 4, 4, 2, 0, 2, 4, 0, 0, 2, 0, 2, 0, 4, 4, 4, 0, 2, 4, 4, 0, 2, 0, 2, 0, 0, 4, 2, 0, 2, 0, 4, 0, 2, 0, 4, 0, 4, 4, 2, 0, 2, 4, 0, 0, 4, 0, 2, 0, 4, 0, 2, 0, 2, 4, 0, 0, 4, 0, 2, 0, 0, 4, 2, 0, 4, 4, 4, 0, 2, 0, 4, 0, 4, 4, 4, 0, 2, 0, 0, 0, 2, 0, 2, 0, 0

Offset: 1

Author

Leroy Quet, Aug 16 2005

Keywords

• nonn

Comments

Depends only on prime signature. - Reinhard Zumkeller, May 24 2010

Examples

			The divisors of 6 are 1, 2, 3 and 6. Of the permutations of these integers, only (6,1,2,3), (6,1,3,2), (2,3,1,6) and (3,2,1,6) are such that every pair of adjacent elements is coprime.
		

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A178254. - Reinhard Zumkeller, May 24 2010

Formula

a(1)=1, a(p) = 2, a(p^2) = 2, a(p*q) = 4 (where p and q are distinct primes), all other terms are 0.

a(A033942(n))=0; a(A037143(n))>0; a(A000430(n))=2; a(A006881(n))=4. - Reinhard Zumkeller, May 24 2010

Extensions

Terms 17 to 59 from Diana L. Mecum, Jul 18 2008

More terms from David Wasserman, Oct 01 2008