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A118680 Numerator of determinant of n X n matrix with M(i,j) = (i+1)/i if i=j otherwise 1.

%I A118680 #8 Aug 14 2012 04:59:38
%S A118680 2,2,7,11,2,11,29,37,23,1,67,79,23,53,11,137,1,43,191,211,29,127,277,
%T A118680 43,163,1,379,37,109,233,71,23,281,149,631,1,1,53,71,821,431,113,947,
%U A118680 991,1,541,1129,107,613,1
%N A118680 Numerator of determinant of n X n matrix with M(i,j) = (i+1)/i if i=j otherwise 1.
%C A118680 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 A118680 Vincenzo Librandi, <a href="/A118680/b118680.txt">Table of n, a(n) for n = 1..10000</a>
%F A118680 a(n) = Numerator[Det[ DiagonalMatrix[ Table[ 1/i, {i, 1, n} ] ] + 1 ]].
%F A118680 a(n) = Numerator[ (1 + Sum[ k, {k,1,n} ]) /Product[ k, {k,1,n} ] ]. a(n) = Numerator[ (1 + n(n+1)/2) / n! ].
%t A118680 Numerator[Table[ Det[ DiagonalMatrix[ Table[ 1/i, {i, 1, n} ] ] + 1 ], {n, 1, 80} ]]
%t A118680 Table[Numerator[(1+n(n+1)/2)/n! ],{n,1,100}]
%Y A118680 Cf. A045373.
%K A118680 frac,nonn
%O A118680 1,1
%A A118680 _Alexander Adamchuk_, May 19 2006, Dec 13 2006