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%I M4745 #58 Feb 16 2024 05:47:40
%S 1,1,10,215,12231,2025462,1351857641,6255560531733
%N Egyptian fractions: number of solutions of 1 = 1/x_1 + ... + 1/x_n in positive integers.
%C Solutions differing only in the order of the x_i are counted as distinct.
%C All denominators in the expansion 1 = 1/x_1 + ... + 1/x_n are bounded by A000058(n-1) = A129871(n). - _Max Alekseyev_, Dec 30 2003
%D R. K. Guy, Unsolved Problems in Number Theory, D11.
%D D. Singmaster, "The number of representations of one as a sum of unit fractions," unpublished manuscript, 1972.
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H Zachary Harris and Joel Louwsma, <a href="https://arxiv.org/abs/1909.02022">On Arithmetical Structures on Complete Graphs</a>, arXiv:1909.02022 [math.NT], 2019. See also <a href="https://doi.org/10.2140/involve.2020.13.345">Involve</a> (2020) Vol. 13, No. 2, 345-355.
%H Claire Levaillant, <a href="https://arxiv.org/abs/2311.03668">On arithmetical structures on K9</a>, arXiv:2311.03668 [math.NT], 2023.
%H Putnam Competition, <a href="http://math.ucsd.edu/~pfitz/pastputnam.html">58th Putnam Mathematical Competition, 1997, Problem A-5</a>
%H D. Singmaster, <a href="/A002966/a002966.pdf">The number of representations of one as a sum of unit fractions</a>, Unpublished M.S., 1972.
%H Carlos E. Valencia and R. R. Villagrán, <a href="https://arxiv.org/abs/2101.05238">Algorithmic aspects of arithmetical structures</a>, arXiv:2101.05238 [math.NT], 2021.
%H <a href="/index/Ed#Egypt">Index entries for sequences related to Egyptian fractions</a>
%e For n=3 the 10 solutions are {2,3,6} (6 ways), {2,4,4} (3 ways), {3,3,3} (1 way).
%Y Cf. A002966, A006585.
%Y Cf. A000058.
%K nonn,nice,hard,more
%O 1,3
%A _N. J. A. Sloane_
%E a(7) from _Jud McCranie_
%E a(8) from John Dethridge, Jan 11 2004
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