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%I #5 Mar 31 2012 13:20:26
%S 1,2,1,13,19,13,17,43,53,1,19,89,103,59,67,151,13,47,1,229,251,137,
%T 149,1,349,47,101,433,463,1,263,43,593,157,83,701,739,389,409,859,53,
%U 59,1,1033,83,563,587,1223,67,331,1,1429,1483,769,797,127,1709,1,457,1889
%N Absolute value of numerator of determinant of n X n matrix with M(i,j) = i/(i+1) if i=j otherwise 1.
%C Numbers n such that a(n) = 1 are listed in A127852.
%C All a(n)>1 are prime belonging to A038889 (i.e., 17 is a square mod a(n)).
%F 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.
%F a(n) = Numerator[(-1)^(n+1) Det[ DiagonalMatrix[ Table[ i/(i+1) - 1, {i, 1, n} ] ] + 1 ]].
%F a(n) = Numerator[ (n^2+3n-2)/(2(n+1)!) ] = Numerator[ ((2n+3)^2-17)/(4(n+1)!) ].
%t Numerator[Table[(-1)^(n+1) Det[ DiagonalMatrix[ Table[ i/(i+1) - 1, {i, 1, n} ] ] + 1 ], {n, 1, 70} ]]
%t Table[ Numerator[ (n^2+3n-2)/(2(n+1)!) ], {n,1,100} ]
%Y Cf. A038889.
%Y Cf. A118680, A127852, A127853.
%K frac,nonn
%O 1,2
%A _Alexander Adamchuk_, May 19 2006, Feb 03 2007
%E Edited by _Max Alekseyev_, Jun 02 2009
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