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A236864
Numbers n such that the sum of the n-th powers of all symmetric 2 X 2 matrices over Z/nZ gives a nonzero matrix.
0
6, 18, 24, 30, 42, 48, 54, 66, 78, 90, 96, 102, 114, 120, 126, 138, 150, 162, 168, 174, 186, 192, 198, 210, 222, 234, 240, 246, 258, 264, 270, 282, 294, 306, 312, 318, 330, 336, 342, 354, 360, 366, 378, 384, 390, 402, 408, 414, 426, 438
OFFSET
1,1
EXAMPLE
For n=6 the sum of 6th powers is [[3,0],[0,3]].
MATHEMATICA
matrices[n_] := matrices[n] = Flatten[Table[{{a, b}, {b, d}}, {a, n}, {b, n}, {d, n}], 2]; su[n_, k_] := su[n, k] = Mod[Sum[MatrixPower[matrices[n][[i]], k], {i, 1, Length[matrices[n]]}], n]; Table[If[! su[n, n] == {{0, 0}, {0, 0}}, Print[n]; n], {n, 1, 120}] // Union
CROSSREFS
Cf. A017953.
Sequence in context: A236359 A011775 A015707 * A372566 A101527 A028887
KEYWORD
nonn,more
AUTHOR
EXTENSIONS
a(12)-a(50) from Giovanni Resta, Feb 01 2014
STATUS
approved