This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A006585 M4281 #51 Feb 21 2024 10:50:55
%S A006585 1,0,1,6,72,2320,245765,151182379
%N A006585 Egyptian fractions: number of solutions to 1 = 1/x_1 + ... + 1/x_n in positive integers x_1 < ... < x_n.
%C A006585 All denominators in the expansion 1 = 1/x_1 + ... + 1/x_n are bounded by A000058(n-1), i.e., 0 < x_1 < ... < x_n < A000058(n-1). Furthermore, for a fixed n, x_i <= (n+1-i)*(A000058(i-1)-1). - _Max Alekseyev_, Oct 11 2012
%C A006585 If on the other hand, x_k need not be unique, see A002966. - _Robert G. Wilson v_, Jul 17 2013
%D A006585 _Marc LeBrun_, personal communication.
%D A006585 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A006585 M. Le Brun, <a href="/A006577/a006577.pdf">Email to N. J. A. Sloane, Jul 1991</a>
%H A006585 S. V. Konyagin, <a href="https://doi.org/10.1134/S0001434614010295">Double exponential lower bound for the number of representations of unity by Egyptian fractions</a>. Mathematical Notes, 95:1-2 (2014), 277-281.
%H A006585 T. D. Browning and C. Elsholtz, <a href="https://doi.org/10.1215/ijm/1359762408">The number of representations of rationals as a sum of unit fractions</a>, Illinois J. Math. 55:2 (2011), 685-696.
%H A006585 Joel Louwsma, <a href="https://arxiv.org/abs/2402.09515">On solutions of Sum_{i=1..n} 1/x_i = 1 in integers of the form 2^a*k^b, where k is a fixed odd positive integer</a>, arXiv:2402.09515 [math.NT], 2024.
%H A006585 <a href="/index/Ed#Egypt">Index entries for sequences related to Egyptian fractions</a>
%F A006585 a(n) = A280520(n,1).
%e A006585 The 6 solutions for n=4 are 2,3,7,42; 2,3,8,24; 2,3,9,18; 2,3,10,15; 2,4,5,20; 2,4,6,12.
%Y A006585 Cf. A000058, A002966, A002967, A280518.
%K A006585 nonn,nice,hard,more
%O A006585 1,4
%A A006585 _N. J. A. Sloane_
%E A006585 a(1)-a(7) are confirmed by _Jud McCranie_, Dec 11 1999
%E A006585 a(8) from John Dethridge (jcd(AT)ms.unimelb.edu.au), Jan 08 2004