A118680 - OEIS

%I #8 Aug 14 2012 04:59:38

%S 2,2,7,11,2,11,29,37,23,1,67,79,23,53,11,137,1,43,191,211,29,127,277,

%T 43,163,1,379,37,109,233,71,23,281,149,631,1,1,53,71,821,431,113,947,

%U 991,1,541,1129,107,613,1

%N Numerator of determinant of n X n matrix with M(i,j) = (i+1)/i if i=j otherwise 1.

%C Some a(n) are equal to 1 (n=10,17,26,36,37,45..). It appears that all other a(n) are primes congruent to {0, 1, 2, 4} mod 7 - A045373.

%H Vincenzo Librandi, <a href="/A118680/b118680.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) = Numerator[Det[ DiagonalMatrix[ Table[ 1/i, {i, 1, n} ] ] + 1 ]].

%F a(n) = Numerator[ (1 + Sum[ k, {k,1,n} ]) /Product[ k, {k,1,n} ] ]. a(n) = Numerator[ (1 + n(n+1)/2) / n! ].

%t Numerator[Table[ Det[ DiagonalMatrix[ Table[ 1/i, {i, 1, n} ] ] + 1 ], {n, 1, 80} ]]

%t Table[Numerator[(1+n(n+1)/2)/n! ],{n,1,100}]

%Y Cf. A045373.

%K frac,nonn

%O 1,1

%A _Alexander Adamchuk_, May 19 2006, Dec 13 2006