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Search: id:A053191
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| 1, 4, 18, 32, 100, 72, 294, 256, 486, 400, 1210, 576, 2028, 1176, 1800, 2048, 4624, 1944, 6498, 3200, 5292, 4840, 11638, 4608, 12500, 8112, 13122, 9408, 23548, 7200, 28830, 16384, 21780, 18496, 29400, 15552, 49284, 25992, 36504, 25600, 67240
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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Number of invertible 2 X 2 symmetric matrices over Z(n). - T. D. Noe (noe(AT)sspectra.com), Jan 13 2006
Note that A115077 gives the number of 2 X 2 symmetric matrices having nonzero determinant. However for composite n a nonzero determinant is not sufficient for the matrix to be invertible; the determinant must also be relatively prime to n. - T. D. Noe (noe(AT)sspectra.com), Jan 13 2006
Also Euler phi function of n^3.
For n^k, EulerPhi[n^k]=n^(k-1)*EulerPhi[n]. The same holds if Phi is replaced by cototient function.
Also the sum of the degrees of the irreducible representations of the group GL(2,Z_n) (sequence A000252). - Sharon Sela (sharonsela(AT)hotmail.com), Feb 06 2002
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FORMULA
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a(n)=n^2*EulerPhi[n]=A000010(n^3)
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EXAMPLE
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n=5: n^3=125, EulerPhi[125]=125-25=100.
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MAPLE
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with(numtheory):a:=n->phi(n^3): seq(a(n), n=1..41); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Oct 07 2007
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MATHEMATICA
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Table[cnt=0; Do[m={{a, b}, {b, c}}; If[Det[m, Modulus->n]>0 && MatrixQ[Inverse[m, Modulus->n]], cnt++ ], {a, 0, n-1}, {b, 0, n-1}, {c, 0, n-1}]; cnt, {n, 2, 50}] - T. D. Noe (noe(AT)sspectra.com), Jan 13 2006
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CROSSREFS
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Cf. A000252 (number of invertible 2 X 2 matrices over Z(n)), A115075, A115076, A115077.
Cf. A000010, A051953, A002618, A053650, A053191, A053192, A001248.
Sequence in context: A033166 A049726 A130656 this_sequence A003474 A095823 A092116
Adjacent sequences: A053188 A053189 A053190 this_sequence A053192 A053193 A053194
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KEYWORD
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nonn,mult
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AUTHOR
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Labos E. (labos(AT)ana.sote.hu), Mar 02 2000
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EXTENSIONS
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Edited by njas at the suggestion of Andrew Plewe, Jun 05 2007
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