Search: id:A118680
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%I A118680
%S A118680 2,2,7,11,2,11,29,37,23,1,67,79,23,53,11,137,1,43,191,211,29,127,277,43,
%T A118680 163,1,379,37,109,233,71,23,281,149,631,1,1,53,71,821,431,113,947,991,
               1,
%U A118680 541,1129,107,613,1,1327,197,179,743,67,1597,827,107,1,1831,1,977,2017
%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.
%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.
%Y A118680 Sequence in context: A054226 A000024 A005223 this_sequence A094116 A079476 
               A005298
%Y A118680 Adjacent sequences: A118677 A118678 A118679 this_sequence A118681 A118682 
               A118683
%K A118680 frac,nonn
%O A118680 1,1
%A A118680 Alexander Adamchuk (alex(AT)kolmogorov.com), May 19 2006, Dec 13 2006

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