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 A118679 Absolute value of numerator of determinant of n X n matrix with M(i,j) = i/(i+1) if i=j otherwise 1. 17
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS 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)). LINKS FORMULA 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)!) ]. MATHEMATICA 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} ] CROSSREFS Cf. A038889. Cf. A118680, A127852, A127853. Sequence in context: A074808 A113097 A032001 * A087451 A063558 A174170 Adjacent sequences:  A118676 A118677 A118678 * A118680 A118681 A118682 KEYWORD frac,nonn AUTHOR Alexander Adamchuk, May 19 2006, Feb 03 2007 EXTENSIONS Edited by Max Alekseyev, Jun 02 2009 STATUS approved

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Last modified June 21 04:10 EDT 2021. Contains 345354 sequences. (Running on oeis4.)