A349086 The number of six-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,u) such that x/y = 1/p + 1/q + 1/r + 1/s + 1/t + 1/u where p, q, r, s, t, and u are integers with p < q < r < s < t < u.

244817, 3421052, 206917, 18420699, 244817, 49938, 64025680, 6462507, 1434759, 41993, 131223239, 3421052, 244817, 206917, 16018, 431008820, 38282319, 3506679, 3879468, 323772, 108276, 681922142, 18420699, 21874941, 244817, 659687, 49938, 45169

Offset: 1

Author

Jud McCranie, Nov 19 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 2) and the columns correspond to the numerators:

x = 1 2 3 4 5 Rationals x/y:

Row 1: (y=2) 244817 1/2

Row 2: (y=3) 3421052 206917 1/3, 2/3

Row 3: (y=4) 18420699 244817 49938 1/4, 2/4, 3/4

Row 4: (y=5) 64025680 6462507 1434759 41993 1/5, 2/5, 3/5, 4/5

Row 5: (y=6) 131223239 3421052 244817 206917 16018 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).

Links

• Jud McCranie, Table of n, a(n) for n = 1..36

Crossrefs

Cf. A241883, A002260, A003057, A349082, A349083, A349084, A349085.