%I M4745
%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(n1)=A129871(n).  _Max Alekseyev_, Dec 30 2003
%D Mohammad K. Azarian, Diophantine Pair, Problem B881, Fibonacci Quarterly, Vol. 37, No. 3, August 1999, pp. 277278. Solution published in Vol. 38, No. 2, May 2000, pp. 183184.
%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%D D. Singmaster, "The number of representations of one as a sum of unit fractions," unpublished manuscript, 1972.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 Putnam Competition, <a href="http://math.ucsd.edu/~pfitz/pastputnam.html">58th Putnam Mathematical Competition, 1997, Problem A5</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, Unpublished M.S., 1972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 <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
