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

%I #28 May 20 2020 02:56:49

%S 0,6,5616,660602880,56653740000000000,847972210819236925066444800,

%T 35832085525362833262818017603275320524800,

%U 454962949457868147194568283111215836246845930653666508800

%N Number of n X n matrices whose determinant is 1 mod n.

%C What is min(a(n) / n^(n^2 - 1)), for n>1 ?. - _Vaclav Kotesovec_, May 19 2020

%H Sean A. Irvine, <a href="https://github.com/archmageirvine/joeis/blob/master/src/irvine/oeis/a011/A011788.java">Java program</a> (github)

%H Vaclav Kotesovec, <a href="/A011788/a011788.jpg">Plot of a(n) / n^(n^2 - 1) for n = 1..1000</a>

%F 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

%t 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 *)

%K nonn

%O 1,2

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

%E More terms from _Vladeta Jovovic_, Jul 20 2004

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Last modified September 18 19:41 EDT 2024. Contains 376002 sequences. (Running on oeis4.)