Permutations: a(k) Coprime To k
Edwin Clark
eclark at math.usf.edu
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,
3459600,60891840,32626944,8048712960,3554067456,
425476094976,320265446400,12474417291264
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
Cloitre
(abcloitre(AT)wanadoo.fr), Aug 23 2002
References D. M. Jackson, The combinatorial interpretation of the Jacobi
identity from Lie algebra, J. Combin. Theory, A 23 (1977),
233-256.
Maybe the reference given here gives some information.
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