cp's OEIS Frontend

A118679 Absolute value of numerator of determinant of n X n matrix with M(i,j) = i/(i+1) if i=j otherwise 1.

%I A118679 #5 Mar 31 2012 13:20:26
%S A118679 1,2,1,13,19,13,17,43,53,1,19,89,103,59,67,151,13,47,1,229,251,137,
%T A118679 149,1,349,47,101,433,463,1,263,43,593,157,83,701,739,389,409,859,53,
%U A118679 59,1,1033,83,563,587,1223,67,331,1,1429,1483,769,797,127,1709,1,457,1889
%N A118679 Absolute value of numerator of determinant of n X n matrix with M(i,j) = i/(i+1) if i=j otherwise 1.
%C A118679 Numbers n such that a(n) = 1 are listed in A127852.
%C A118679 All a(n)>1 are prime belonging to A038889 (i.e., 17 is a square mod a(n)).
%F A118679 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 A118679 a(n) = Numerator[(-1)^(n+1) Det[ DiagonalMatrix[ Table[ i/(i+1) - 1, {i, 1, n} ] ] + 1 ]].
%F A118679 a(n) = Numerator[ (n^2+3n-2)/(2(n+1)!) ] = Numerator[ ((2n+3)^2-17)/(4(n+1)!) ].
%t A118679 Numerator[Table[(-1)^(n+1) Det[ DiagonalMatrix[ Table[ i/(i+1) - 1, {i, 1, n} ] ] + 1 ], {n, 1, 70} ]]
%t A118679 Table[ Numerator[ (n^2+3n-2)/(2(n+1)!) ], {n,1,100} ]
%Y A118679 Cf. A038889.
%Y A118679 Cf. A118680, A127852, A127853.
%K A118679 frac,nonn
%O A118679 1,2
%A A118679 _Alexander Adamchuk_, May 19 2006, Feb 03 2007
%E A118679 Edited by _Max Alekseyev_, Jun 02 2009