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

1,2

Comments

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

Links

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

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

Example

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.

Crossrefs

Cf. A178254. - Reinhard Zumkeller, May 24 2010

Sequence in context: A306653 A132003 A122857 * A365498 A367515 A122066

Adjacent sequences: A109807 A109808 A109809 * A109811 A109812 A109813

Keyword

nonn

Author

Leroy Quet, Aug 16 2005

Extensions

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

More terms from David Wasserman, Oct 01 2008

Status

approved