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