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A005326 Permanent of `coprime?' matrix.
(Formerly M2382)
6
1, 1, 3, 4, 28, 16, 256, 324, 3600, 3600, 129744, 63504, 3521232, 3459600, 60891840, 91240704, 8048712960, 3554067456, 425476094976, 320265446400, 12474417291264, 16417666704384, 2778580249611264, 1142807773593600, 172593628397420544 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

Number of permutations p of (1,2,3,...,n) such that k and p(k) are relatively prime for all k in (1,2,3,...,n). - Benoit Cloitre, Aug 23 2002

Coprime matrix M=[m(i,j)] is a square matrix defined by m(i,j)=1 if gcd(i,j)=1 else 0.

REFERENCES

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

LINKS

Seiichi Manyama, Table of n, a(n) for n = 1..30 calculated by Herman Jamke's code.

D. M. Jackson, The combinatorial interpretation of the Jacobi identity from Lie algebra, J. Combin. Theory, A 23 (1977), 233-256.

FORMULA

a(2n) = A009679(n)^2. - T. D. Noe, Feb 10 2007

MATHEMATICA

perm[m_?MatrixQ] := With[{v = Array[x, Length[m]]}, Coefficient[Times @@ (m.v), Times @@ v]]; a[n_] := perm[ Table[ Boole[GCD[i, j] == 1], {i, 1, n}, {j, 1, n}]]; Table[an = a[n]; Print[an]; an, {n, 1, 24}](* Jean-François Alcover, Nov 15 2011 *)

(* or, if version >= 10: *)

a[n_] := Permanent[Table[Boole[GCD[i, j] == 1], {i, 1, n}, {j, 1, n}]]; Table[an = a[n]; Print[an]; an, {n, 1, 24}] (* Jean-François Alcover, Jul 25 2017 *)

PROG

(PARI) permRWNb(a)=n=matsize(a)[1]; if(n==1, return(a[1, 1])); sg=1; nc=0; in=vectorv(n); x=in; x=a[, n]-sum(j=1, n, a[, j])/2; p=prod(i=1, n, x[i]); for(k=1, 2^(n-1)-1, sg=-sg; j=valuation(k, 2)+1; z=1-2*in[j]; in[j]+=z; nc+=z; x+=z*a[, j]; p+=prod(i=1, n, x[i], sg)); return(2*(2*(n%2)-1)*p)

for(n=1, 26, a=matrix(n, n, i, j, gcd(i, j)==1); print1(permRWNb(a)", ")) \\ Herman Jamke (hermanjamke(AT)fastmail.fm), May 13 2007

CROSSREFS

Sequence in context: A042829 A232110 A140896 * A298561 A226049 A100600

Adjacent sequences:  A005323 A005324 A005325 * A005327 A005328 A005329

KEYWORD

nonn,nice

AUTHOR

N. J. A. Sloane

EXTENSIONS

Corrected by Vladeta Jovovic, Jul 05 2003

More terms from T. D. Noe, Feb 10 2007

a(25) from Alois P. Heinz, Nov 15 2016

STATUS

approved

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Last modified January 15 20:47 EST 2019. Contains 319184 sequences. (Running on oeis4.)