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A059479
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Number of 3 X 3 matrices with elements from {0,...,n-1} such that the middle element of each of the eight lines of three (rows, columns and diagonals) is the square (mod n) of the difference of the end elements.
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0
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1, 4, 9, 64, 25, 36, 49, 256, 729, 100, 121, 576, 169, 196, 225, 4096, 289, 2916, 361, 1600, 441, 484, 529, 2304, 15625, 676, 6561, 3136, 841, 900, 961, 16384, 1089, 1156, 1225, 46656, 1369, 1444, 1521, 6400, 1681, 1764, 1849, 7744, 18225, 2116, 2209
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| This sequence is multiplicative. - Mitch Harris, Apr 19 2005
The sequence enumerates the solutions of a system of polynomials equations modulo n, hence is multiplicative by the Chinese Remainder Theorem. The middle entry of the 3 X 3 is zero modulo n. - Michael Somos Apr 30 2005
Multiplicative with a(p^e) = p^(3e - (e % 2)). Mitch Harris (Harris.Mitchell(AT)mgh.harvard.edu) Jun 09, 2005.
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FORMULA
| a(n)=A008833(n)*n^2, where A008833(n) is the largest square that divides n.
Dirichlet g.f.: zeta(s-2)*zeta(2s-6)/zeta(2s-4). - R. J. Mathar, Mar 30 2011
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PROG
| (PARI) a(n)=if(n<1, 0, n^3/core(n)) /* Michael Somos Apr 30 2005 */
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CROSSREFS
| Sequence in context: A002942 A028908 A073658 * A094083 A168251 A062758
Adjacent sequences: A059476 A059477 A059478 * A059480 A059481 A059482
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KEYWORD
| nonn,mult
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AUTHOR
| John W. Layman (layman(AT)math.vt.edu), Feb 15 2001
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