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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.

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

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

Table of n, a(n) for n=1..60.

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: A113097 A032001 A358205 * A087451 A063558 A174170

Adjacent sequences: A118676 A118677 A118678 * A118680 A118681 A118682

KEYWORD

frac,nonn