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%I #10 Aug 29 2019 13:09:59
%S 2,3,4,3,2,5,6,5,4,3,2,7,5,3,8,7,5,4,2,9,7,3,10,9,8,7,6,5,4,3,2,11,7,
%T 5,12,11,10,9,8,7,6,5,4,3,2,13,11,9,5,3,14,13,11,8,7,4,2,15,13,11,9,7,
%U 5,3,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,17,13,11,7,5,18,17,16,15,14,13,12
%N Denominators of array which counts positive rational numbers (not including natural numbers).
%C Numerators are given by A111879.
%C The method to obtain the rationals r(n,k) for row n is described under A111879.
%D P. Dienes, The Taylor Series, Dover 1957, p. 8, eq.(1).
%H W. Lang, <a href="/A111879/a111879.txt">Array of ratios and more.</a>
%F a(n, k)=denominator(r(n, k)), n>=3, k=1..phi(n)-1, with phi(n):=A000010(n) (Euler's totient function) and the ratios r(n, k) are defined for row n in A111879.
%e [2], [3], [4, 3, 2], [5], [6, 5, 4, 3, 2], [7, 5, 3], [8, 7, 5, 4,
%e 2], [9, 7, 3],...
%e The corresponding rationals are: [1/2], [1/3], [1/4, 2/3, 3/2],
%e [1/5], [1/6, 2/5, 3/4, 4/3, 5/2], [1/7, 3/5, 5/3], [1/8, 2/7, 4/5, 5/4, 7/2],
%e [1/9, 3/7, 7/3],...
%Y Cf. A020652/A020653 if natural numbers are included.
%K nonn,easy,frac,tabf
%O 3,1
%A _Wolfdieter Lang_, Aug 23 2005
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