A011788 Number of n X n matrices whose determinant is 1 mod n.

0, 6, 5616, 660602880, 56653740000000000, 847972210819236925066444800, 35832085525362833262818017603275320524800, 454962949457868147194568283111215836246845930653666508800

Offset

1,2

Comments

What is min(a(n) / n^(n^2 - 1)), for n>1 ?. - Vaclav Kotesovec, May 19 2020

Links

Table of n, a(n) for n=1..8.

Sean A. Irvine, Java program (github)

Vaclav Kotesovec, Plot of a(n) / n^(n^2 - 1) for n = 1..1000

Formula

a(n) = (n^(n^2) / phi(n)) * Product_{primes p dividing n} (Product_{k=1..n} (1 - 1/p^k)) for n > 1, a(1)=0. - Sean A. Irvine, Jun 26 2018

Mathematica

Join[{0}, Table[n^(n^2) / EulerPhi[n] * Product[QPochhammer[1/p, 1/p, n], {p, Select[Divisors[n], PrimeQ]}], {n, 2, 10}]] (* Vaclav Kotesovec, May 19 2020 *)

Crossrefs

Sequence in context: A116117 A116135 A367958 * A320446 A172649 A111152

Adjacent sequences: A011785 A011786 A011787 * A011789 A011790 A011791

Keyword

nonn

Author

Benjamin T. Love (benlove(AT)preston.polaristel.net)

Extensions

More terms from Vladeta Jovovic, Jul 20 2004

Status

approved