Search: id:A000252
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%I A000252
%S A000252 1,6,48,96,480,288,2016,1536,3888,2880,13200,4608,26208,12096,23040,
%T A000252 24576,78336,23328,123120,46080,96768,79200,267168,73728,300000,157248,
%U A000252 314928,193536,682080,138240,892800,393216,633600,470016,967680,373248
%N A000252 Number of invertible 2 X 2 matrices mod n.
%C A000252 For a prime p, a(p) = (p^2 - 1)*(p^2 - p) (this is the order of GL(2,
               p)). More generally a(n) is multiplicative: if the canonical factorization 
               of n is the product of p^e(p) over primes p then a(n) = product ((p^(2*e(p)) 
               - p^(2*e(p) - 2)) * (p^(2*e(p)) - p^(2*e(p) - 1))). - Brian Wallace 
               (wallacebrianedward(AT)yahoo.co.uk), Apr 05 2001, Dan Fux (dan.fux(AT)OpenGaia.com 
               or danfux(AT)OpenGaia.com), Apr 18 2001
%H A000252 T. D. Noe, <a href="b000252.txt">Table of n, a(n) for n=1..1000</a>
%H A000252 J. Overbey, W. Traves and J. Wojdylo, <a href="http://jeff.over.bz/papers/
               undergrad/on-the-keyspace-of-the-hill-cipher.pdf">On the Keyspace 
               of the Hill Cipher</a>
%F A000252 a(n) = n^4 * product (1-1/p^2)*(1-1/p) = n^4 * product p^(-3)(p^2 - 1)*(p 
               - 1) where the product is over all the primes p that divide n. - 
               Dan Fux (dan.fux(AT)OpenGaia.com or danfux(AT)OpenGaia.com), Apr 
               18 2001
%F A000252 Multiplicative with a(p^e) = (p-1)^2*(p+1)*p^(4e-3). - David W. Wilson 
               (davidwwilson(AT)comcast.net), Aug 01, 2001.
%F A000252 a(n) = A000056(n)*phi(n), where phi is Euler totient function (cf. A000010). 
               - Vladeta Jovovic (vladeta(AT)eunet.rs), Oct 30 2001
%Y A000252 The number of 2 X 2 matrices mod n with determinant 1 is A000056. The 
               order of GL_2(K) for a finite field K is in sequence A059238.
%Y A000252 Cf. A011785, A064767.
%Y A000252 Sequence in context: A015553 A071878 A104256 this_sequence A078237 A052651 
               A153796
%Y A000252 Adjacent sequences: A000249 A000250 A000251 this_sequence A000253 A000254 
               A000255
%K A000252 nonn,easy,nice,mult
%O A000252 1,2
%A A000252 N. J. A. Sloane (njas(AT)research.att.com).
%E A000252 More terms from David W. Wilson (davidwwilson(AT)comcast.net), Jul 21, 
               2001

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