OFFSET
1,1
COMMENTS
The sequence are the terms in a triangle, where the rows correspond to the denominator of the rational number (starting with row 2, column 1) and the columns correspond to the numerators:
x= 1 2 3 4 5 Rationals x/y:
Row 1: (y=2) 71 1/2
Row 2: (y=3) 272, 61 1/3, 2/3
Row 3: (y=4) 586, 71, 27 1/4, 2/4, 3/4
Row 4: (y=5) 978, 275, 122, 18 1/5, 2/5, 3/5, 4/5
Row 5: (y=6) 1591, 272, 71, 61, 17 1/6, 2/6, 3/6, 4/6, 5/6
Alternatively, order the rational numbers, x/y, 0 < x/y < 1, in this order: 1/2, 1/3, 2/3, 1/4, 2/4, 3/4, 1/5, 2/5, ... The numerators of the n-th rational number are A002260(n) and the denominators are A003057(n).
Column 1 is A241883.
LINKS
Jud McCranie, Table of n, a(n) for n = 1..990
EXAMPLE
The 10th rational number under this ordering is 4/5; 4/5 has 18 representations as the sum of four distinct unit fractions, so a(10) = 18:
4/5 = 1/2 + 1/4 + 1/21 + 1/420
= 1/2 + 1/4 + 1/22 + 1/220
... 15 solutions omitted
= 1/3 + 1/5 + 1/6 + 1/10
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Jud McCranie, Nov 11 2021
STATUS
approved