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A066907 Number of elements in GL(2,Z_n) x with x^2 == I mod n where I is the identity matrix. 5

%I

%S 1,4,14,28,32,56,58,176,110,128,134,392,184,232,448,608,308,440,382,

%T 896,812,536,554,2464,752,736,974,1624,872,1792,994,2336,1876,1232,

%U 1856,3080,1408,1528,2576,5632,1724,3248,1894,3752,3520,2216,2258,8512,2746

%N Number of elements in GL(2,Z_n) x with x^2 == I mod n where I is the identity matrix.

%C a(n) is multiplicative and for an odd prime power p^k : a(p^k) = 2 + p^(2k-1)(p+1). [corrected by _Felix A. Pahl_, Mar 08 2013]

%C Number of involutory matrices mod n. - _Charles R Greathouse IV_, May 29 2013

%H Charles R Greathouse IV, <a href="/A066907/b066907.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) = A066947(n) + 1.

%o (PARI) a(n)=my(o=valuation(n,2),f=factor(n>>o)); prod(i=1,#f[,1],f[i,1]^(2*f[i,2])+f[i,1]^(2*f[i,2]-1)+2)*if(o, if(o>1, if(o>2, 9*4^(o-1)+32,28),4),1) \\ _Charles R Greathouse IV_, May 29 2013

%Y Cf. A066947, A060594.

%K nonn,mult,easy

%O 1,2

%A Sharon Sela (sharonsela(AT)hotmail.com), Jan 26 2002

%E Added more terms (from A066947), _Joerg Arndt_, Mar 08 2013

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Last modified August 9 01:35 EDT 2020. Contains 336310 sequences. (Running on oeis4.)