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A111880 Denominators of array which counts positive rational numbers (not including natural numbers).

%I A111880 #17 Jan 21 2025 03:26:21
%S A111880 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 A111880 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 A111880 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 A111880 Denominators of array which counts positive rational numbers (not including natural numbers).
%C A111880 Numerators are given by A111879.
%C A111880 The method to obtain the rationals r(n,k) for row n is described under A111879.
%D A111880 P. Dienes, The Taylor Series, Dover 1957, p. 8, eq.(1).
%H A111880 Wolfdieter Lang, <a href="/A111879/a111879.txt">Array of ratios and more.</a>
%F A111880 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 A111880 Triangle begins:
%e A111880   [2],
%e A111880   [3],
%e A111880   [4, 3, 2],
%e A111880   [5],
%e A111880   [6, 5, 4, 3, 2],
%e A111880   [7, 5, 3],
%e A111880   [8, 7, 5, 4, 2],
%e A111880   [9, 7, 3],
%e A111880   ...
%e A111880 The corresponding rationals are:
%e A111880   [1/2],
%e A111880   [1/3],
%e A111880   [1/4, 2/3, 3/2],
%e A111880   [1/5],
%e A111880   [1/6, 2/5, 3/4, 4/3, 5/2],
%e A111880   [1/7, 3/5, 5/3],
%e A111880   [1/8, 2/7, 4/5, 5/4, 7/2],
%e A111880   [1/9, 3/7, 7/3],
%e A111880   ...
%Y A111880 Cf. A020652/A020653 if natural numbers are included.
%Y A111880 Cf. A111879.
%K A111880 nonn,easy,frac,tabf
%O A111880 3,1
%A A111880 _Wolfdieter Lang_, Aug 23 2005