login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

Noninvertible 3 X 3 matrices over Z_n.
1

%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