A349085 - OEIS

%I #36 Dec 05 2021 05:39:32

%S 2293,15304,1890,47314,2293,662,112535,19311,6650,510,190665,15304,

%T 2293,1890,298,368474,64992,10447,11362,1666,708,577623,47314,44843,

%U 2293,3820,662,489,925336,147545,15304,5302,18606,1890,850,277,1164976,112535,39798,19311,2293,6650,1152

%N 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.

%C 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:

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

%C Row 1: (y=2)    2293                            1/2

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

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

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

%C Row 5: (y=6)  190665, 15304, 2293, 1890, 298    1/6, 2/6, 3/6, 4/6, 5/6

%C 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).

%C Column 1 is A347566, skipping the first term.

%H Jud McCranie, <a href="/A349085/b349085.txt">Table of n, a(n) for n = 1..990</a>

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

%K nonn,tabl

%O 1,1

%A _Jud McCranie_, Nov 13 2021