cp's OEIS Frontend

A144063 Egyptian fractions: number of solutions of 1 = 1/x_1 + ... + 1/x_n in positive integers x_1 < ... < x_n <= 256.

%I A144063 #21 Feb 16 2025 08:33:08
%S A144063 1,0,1,6,62,642,5623,47126,368680,2715613,18876751,124137535,
%T A144063 774232619,4595291801,26030660449,141031079451,731862267491,
%U A144063 3641135367129,17379359388167,79633646141291,350541406992141,1483638948734104,6043258919626951,23713645892145709
%N A144063 Egyptian fractions: number of solutions of 1 = 1/x_1 + ... + 1/x_n in positive integers x_1 < ... < x_n <= 256.
%C A144063 Egyptian fraction for a rational number is to represent the number in sum of some distinct unit fraction, such as 1 = 1/2 + 1/3 + 1/6, here we represent 1 by a three terms Egyptian fraction and the largest denominator is 6. And the representation is non-unique.
%C A144063 There are a total of 3007198863516917545589795267613 Egyptian fractions for 1 whose largest denominator is no more than 256.
%H A144063 Jinyuan Wang, <a href="/A144063/b144063.txt">Table of n, a(n) for n = 1..114</a>
%H A144063 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/EgyptianFraction.html">Egyptian Fraction</a>
%H A144063 <a href="http://bbs.emath.ac.cn/viewthread.php?tid=223&amp;page=7&amp;fromuid=20#pid1591">link for the result</a> [Broken link]
%F A144063 a(n) = 0 for n > 114.
%e A144063 a(1)=1 since 1 = 1/1.
%e A144063 a(2)=0 since the sum of any two distinct unit fractions are not 1.
%e A144063 a(3)=1 since the only three terms Egyptian fraction for 1 is 1/2 + 1/3 + 1/6.
%Y A144063 Cf. A002967, A006585.
%K A144063 nonn,fini
%O A144063 1,4
%A A144063 _Zhao Hui Du_, Sep 09 2008