%I #9 Aug 03 2024 07:09:39

%S 0,344,8451,176128,465125,8190720,6569479,90177536,166341033,

%T 750016000,233671691,4193648640,878081581,14985313280,21730143375,

%U 46170898432,7384597649,161217941760,17874835219,384008192000,414816720885

%N Noninvertible 3 X 3 matrices over Z_n.

%H T. D. Noe, <a href="/A065499/b065499.txt">Table of n, a(n) for n=1..1000</a>

%F a(n) = n^9 - A064767(n) = n^9 - n^9 * Product (1-1/p^3)*(1-1/p^2)*(1-1/p) where the product is over all the primes p that divide n.

%t f[n_] := (g = First[ Transpose[ FactorInteger[n]]]; n^9*(1 - Apply[ Times, 1 - 1/g] Apply[ Times, 1 - 1/g^2] Apply[ Times, 1 - 1/g^3])); Table[ f[n], {n, 1, 22} ]

%o (PARI) a(n) = {my(f = factor(n), p = f[,1], e=f[,2]); n^9 - prod(k = 1, #p, (p[k]-1)*(p[k]^2-1)*(p[k]^3-1)*(p[k]^(9*e[k]-6)));} \\ _Amiram Eldar_, Aug 03 2024

%Y Cf. A064767, A020479, A000252.

%K nonn

%O 1,2

%A Dan Fux (dan.fux(AT)OpenGaia.com or danfux(AT)OpenGaia.com), Nov 25 2001

%E More terms from _Robert G. Wilson v_, Nov 30 2001