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A002967 Egyptian fractions: number of solutions of 1 = 1/x_1 + ... + 1/x_n in positive integers.
(Formerly M4745)
6

%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(n-1)=A129871(n). - _Max Alekseyev_, Dec 30 2003

%D Mohammad K. Azarian, Diophantine Pair, Problem B-881, Fibonacci Quarterly, Vol. 37, No. 3, August 1999, pp. 277-278. Solution published in Vol. 38, No. 2, May 2000, pp. 183-184.

%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%D D. Singmaster, "The number of representations of one as a sum of unit fractions," unpublished manuscript, 1972.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 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, Unpublished M.S., 1972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 <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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Last modified June 17 07:00 EDT 2019. Contains 324183 sequences. (Running on oeis4.)