Permutations: a(k) Coprime To k

Edwin Clark eclark at
Wed Apr 23 05:57:23 CEST 2003

On Sat, 22 Mar 2003, Leroy Quet wrote:

> What is the number of permutations, {a(1),a(2),a(3),...,a(m)}, of
> {1,2,3,...,m} where each a(k) is relatively prime to each k, for 1 <=
> k <= m?
> Is there an easy way to calculate this counting-sequence directly?

This is sequence:

ID Number: A005326 (Formerly M2382)
Sequence:  1,1,3,4,28,16,256,324,3600,3600,129774,63504,3521232,
Name:      Permanent of `coprime?' matrix.
Comments:  Number of perumutations p of (1,2,3,...,n) such that k and
p(k) are
              relatively primes for any k in (1,2,3,...,n) - Benoit
              (abcloitre(AT), Aug 23 2002
References D. M. Jackson, The combinatorial interpretation of the Jacobi
              identity from Lie algebra, J. Combin. Theory, A 23 (1977),

Maybe the reference given here gives some information.

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