A245678 Denominator of sum of fractions A182972(k) / A182973(k) such that A182972(k) + A182973(k) = n.

2, 3, 12, 5, 60, 35, 280, 63, 2520, 77, 27720, 1287, 8008, 6435, 144144, 2431, 2450448, 46189, 3695120, 146965, 232792560, 96577, 1070845776, 1300075, 2974571600, 5014575, 11473347600, 215441, 332727080400, 31556720475, 486207248800, 20419054425

Offset: 3

Author

Reinhard Zumkeller, Jul 30 2014

Keywords

• nonn
• frac

Comments

A182972(n) and A182973(n) provide an enumeration of positive rationals < 1 arranged by increasing sum of numerator and denominator then by increasing numerator;

a(n) = denominator(sum(A182972(k)/A182973(k): k such that A182972(k)+A182973(k)=n));

A245718(n) = floor(A245677(n)/a(n)).

Examples

			See A245677.
		

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 3..1000
• Paul Yiu, Recreational Mathematics, 24.3.1 Appendix: Two enumerations of the rational numbers in (0,1), page 633.

Crossrefs

Cf. A245677 (numerator), A182972, A182973, A245718.

Programs

Haskell

import Data.Ratio ((%), denominator)
a245678 n = denominator $ sum
   [num % den | num <- [1 .. div n 2], let den = n - num, gcd num den == 1]