%I A062270
%S A062270 3,45,175,693,11011,2807805,302307005,402243205,714186915,42803602439,
%T A062270 11086133031701,5908908905896633,1488200914442251997,
%U A062270 3041106216468949733,16213234917387714257,21611220383343195817
%N A062270 Numerators in partial products of the twin prime constant.
%C A062270 For n>1, a(n) is the absolute value of the numerator of the determinant 
               of the n X n matrix with elements M[i,j] = 1/(Prime[i]-1)^2 for i=j 
               and 1 otherwise. - Alexander Adamchuk (alex(AT)kolmogorov.com), Jun 
               02 2006
%D A062270 S. R. Finch, Mathematical Constants, Cambridge, 2003, pp. 84-94.
%D A062270 G. H. Hardy and E. M. Wright, An Introduction to the Theory of Numbers, 
               5th ed., Oxford Univ. Press, 1979, ch. 22.20
%H A062270 S. R. Finch, <a href="http://algo.inria.fr/bsolve/constant/hrdyltl/hrdyltl.html">
               Hardy-Littlewood constants</a>
%F A062270 a(n)= a(n-1)*(p(n)*(p(n)-2)) / gcd( a(n-1)*p(n)*(p(n)-2), A062271(n)) 
               for n > 2.
%e A062270 a(4)= 175= 3*1*5*3*7*5 / gcd( 3*1*5*3*7*5, 2*2*4*4*6*6 ).
%t A062270 Numerator[Abs[Table[ Det[ DiagonalMatrix[ Table[ 1/(Prime[i]-1)^2 - 1, 
               {i, 1, n} ] ] + 1 ], {n, 2, 20} ]]] - Alexander Adamchuk (alex(AT)kolmogorov.com), 
               Jun 02 2006
%Y A062270 A062271 (denominators), A005597 (decimal expansion).
%Y A062270 Sequence in context: A075320 A071968 A093585 this_sequence A069955 A062346 
               A002682
%Y A062270 Adjacent sequences: A062267 A062268 A062269 this_sequence A062271 A062272 
               A062273
%K A062270 easy,nonn
%O A062270 2,1
%A A062270 Frank.Ellermann(AT)t-online.de, Jun 16 2001
%E A062270 Typo in link corrected by Martin Griffiths (griffm(AT)essex.ac.uk), Apr 
               03 2009