cp's OEIS Frontend

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.

%I A349086 #28 Dec 05 2021 05:39:39
%S A349086 244817,3421052,206917,18420699,244817,49938,64025680,6462507,1434759,
%T A349086 41993,131223239,3421052,244817,206917,16018,431008820,38282319,
%U A349086 3506679,3879468,323772,108276,681922142,18420699,21874941,244817,659687,49938,45169
%N 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.
%C A349086 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:
%C A349086                   x = 1       2       3      4     5   Rationals x/y:
%C A349086 Row 1: (y=2)     244817                                1/2
%C A349086 Row 2: (y=3)    3421052  206917                        1/3, 2/3
%C A349086 Row 3: (y=4)   18420699  244817   49938                1/4, 2/4, 3/4
%C A349086 Row 4: (y=5)   64025680 6462507 1434759  41993         1/5, 2/5, 3/5, 4/5
%C A349086 Row 5: (y=6)  131223239 3421052  244817 206917 16018   1/6, 2/6, 3/6, 4/6, 5/6
%C A349086 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).
%H A349086 Jud McCranie, <a href="/A349086/b349086.txt">Table of n, a(n) for n = 1..36</a>
%Y A349086 Cf. A241883, A002260, A003057, A349082, A349083, A349084, A349085.
%K A349086 nonn,tabl
%O A349086 1,1
%A A349086 _Jud McCranie_, Nov 19 2021