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A245677 Numerator of sum of fractions A182972(k) / A182973(k) such that A182972(k) + A182973(k) = n.

%I A245677 #5 Jul 30 2014 16:58:59
%S A245677 1,1,11,1,79,26,339,34,5297,62,69071,1165,11723,9844,471181,2625,
%T A245677 8960447,73244,8231001,243757,1031626241,151100,4178462515,2651758,
%U A245677 10396147563,11843614,64166447971,362476,1989542332021,97275764008,1830230212061,57286319768
%N A245677 Numerator of sum of fractions A182972(k) / A182973(k) such that A182972(k) + A182973(k) = n.
%C A245677 A182972(n) and A182973(n) provide an enumeration of positive rationals < 1 arranged by increasing sum of numerator and denominator then by increasing numerator;
%C A245677 a(n) = numerator(sum(A182972(k)/A182973(k): k such that A182972(k)+A182973(k)=n));
%C A245677 A245718(n) = floor(a(n)/A245678(n)).
%H A245677 Reinhard Zumkeller, <a href="/A245677/b245677.txt">Table of n, a(n) for n = 3..1000</a>
%H A245677 Paul Yiu, <a href="http://math.fau.edu/Yiu/RecreationalMathematics2003.pdf">Recreational Mathematics</a>, 24.3.1 Appendix: Two enumerations of the rational numbers in (0,1), page 633.
%e A245677 .     |  (num, den) = (A182973, A182973) | num(sum)| den(sum)|   [sum]
%e A245677 .   n |  num/den,   num + den = n        | A245677 | A245678 | A245718
%e A245677 . ----+----------------------------------+---------+---------+--------
%e A245677 .   3 |  1/2                             |       1 |       2 |       0
%e A245677 .   4 |  1/3                             |       1 |       3 |       0
%e A245677 .   5 |  1/4, 2/3                        |      11 |      12 |       0
%e A245677 .   6 |  1/5                             |       1 |       5 |       0
%e A245677 .   7 |  1/6, 2/5, 3/4                   |      79 |      60 |       1
%e A245677 .   8 |  1/7, 3/5                        |      26 |      35 |       0
%e A245677 .   9 |  1/8, 2/7, 4/5                   |     339 |     280 |       1
%e A245677 .  10 |  1/9, 3/7                        |      34 |      63 |       0
%e A245677 .  11 |  1/10, 2/9, 3/8, 4/7, 5/6        |    5297 |    2520 |       2
%e A245677 .  12 |  1/11, 5/7                       |      62 |      77 |       0
%e A245677 .  13 |  1/12, 2/11, 3/10, 4/9, 5/8, 6/7 |   69071 |   27720 |       2
%e A245677 .  14 |  1/13, 3/11, 5/9                 |    1165 |    1287 |       0
%e A245677 .  15 |  1/14, 2/13, 4/11, 7/8           |   11723 |    8008 |       1
%e A245677 .  16 |  1/15, 3/13, 5/11, 7/9           |    9844 |    6435 |       1 .
%o A245677 (Haskell)
%o A245677 import Data.Ratio ((%), numerator)
%o A245677 a245677 n = numerator $ sum
%o A245677    [num % den | num <- [1 .. div n 2], let den = n - num, gcd num den == 1]
%Y A245677  Cf. A245678 (denominator), A182972, A182973, A245718.
%K A245677 nonn,frac
%O A245677 3,3
%A A245677 _Reinhard Zumkeller_, Jul 30 2014