A349085 The number of five-term Egyptian fractions of rational numbers, x/y, 0 < x/y < 1, ordered as below. The sequence is the number of (p,q,r,s,t) such that x/y = 1/p + 1/q + 1/r + 1/s + 1/t where p, q, r, s, and t are integers with p < q < r < s < t.

2293, 15304, 1890, 47314, 2293, 662, 112535, 19311, 6650, 510, 190665, 15304, 2293, 1890, 298, 368474, 64992, 10447, 11362, 1666, 708, 577623, 47314, 44843, 2293, 3820, 662, 489, 925336, 147545, 15304, 5302, 18606, 1890, 850, 277, 1164976, 112535, 39798, 19311, 2293, 6650, 1152

Offset: 1

Author

Jud McCranie, Nov 13 2021

Keywords

• nonn
• tabl

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) 2293 1/2

Row 2: (y=3) 15304, 1890 1/3, 2/3

Row 3: (y=4) 47314, 2293, 662 1/4, 2/4, 3/4

Row 4: (y=5) 112535, 19311, 6650, 510 1/5, 2/5, 3/5, 4/5

Row 5: (y=6) 190665, 15304, 2293, 1890, 298 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 A347566, skipping the first term.

Links

• Jud McCranie, Table of n, a(n) for n = 1..990

Crossrefs

Cf. A241883, A002260, A003057, A349082, A349083, A349084.