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A118679
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Absolute value of numerator of determinant of n X n matrix with M(i,j) = i/(i+1) if i=j otherwise 1.
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17
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1, 2, 1, 13, 19, 13, 17, 43, 53, 1, 19, 89, 103, 59, 67, 151, 13, 47, 1, 229, 251, 137, 149, 1, 349, 47, 101, 433, 463, 1, 263, 43, 593, 157, 83, 701, 739, 389, 409, 859, 53, 59, 1, 1033, 83, 563, 587, 1223, 67, 331, 1, 1429, 1483, 769, 797, 127, 1709, 1, 457, 1889
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OFFSET
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1,2
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COMMENTS
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Numbers n such that a(n) = 1 are listed in A127852.
All a(n)>1 are prime belonging to A038889 (i.e., 17 is a square mod a(n)).
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LINKS
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FORMULA
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det(M) = (-1)^(n+1)*(n^2+3*n-2)/(2*(n+1)!), implying that a(n)=p, where p=A006530(n^2+3*n-2) is the largest prime divisor of (n^2+3*n-2), if p>n+1 or p=sqrt((n^2+3*n-2)/2); otherwise a(n)=1.
a(n) = Numerator[(-1)^(n+1) Det[ DiagonalMatrix[ Table[ i/(i+1) - 1, {i, 1, n} ] ] + 1 ]].
a(n) = Numerator[ (n^2+3n-2)/(2(n+1)!) ] = Numerator[ ((2n+3)^2-17)/(4(n+1)!) ].
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MATHEMATICA
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Numerator[Table[(-1)^(n+1) Det[ DiagonalMatrix[ Table[ i/(i+1) - 1, {i, 1, n} ] ] + 1 ], {n, 1, 70} ]]
Table[ Numerator[ (n^2+3n-2)/(2(n+1)!) ], {n, 1, 100} ]
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CROSSREFS
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KEYWORD
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frac,nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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