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Search: id:A059479
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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
1
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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; listen)
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OFFSET
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1,2
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COMMENT
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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
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a(n)=s*n^2, where s is the largest square that divides n.
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PROGRAM
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(PARI) a(n)=if(n<1, 0, n^3/core(n)) /* Michael Somos Apr 30 2005 */
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CROSSREFS
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Adjacent sequences: A059476 A059477 A059478 this_sequence A059480 A059481 A059482
Sequence in context: A002942 A028908 A073658 this_sequence A094083 A062758 A028822
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KEYWORD
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nonn,mult
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AUTHOR
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John W. Layman (layman(AT)math.vt.edu), Feb 15 2001
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