A065499 Noninvertible 3 X 3 matrices over Z_n.

0, 344, 8451, 176128, 465125, 8190720, 6569479, 90177536, 166341033, 750016000, 233671691, 4193648640, 878081581, 14985313280, 21730143375, 46170898432, 7384597649, 161217941760, 17874835219, 384008192000, 414816720885

Offset: 1

Author

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

Keywords

• nonn

Links

• T. D. Noe, Table of n, a(n) for n=1..1000

Crossrefs

Cf. A064767, A020479, A000252.

Programs

Mathematica

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} ]

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

Formula

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.

Extensions

More terms from Robert G. Wilson v, Nov 30 2001