

A006585


Egyptian fractions: number of solutions to 1 = 1/x_1 + ... + 1/x_n in positive integers x_1 < ... < x_n.
(Formerly M4281)


10




OFFSET

1,4


COMMENTS

All denominators in the expansion 1 = 1/x_1 + ... + 1/x_n are bounded by A000058(n1), i.e., 0 < x_1 < ... < x_n < A000058(n1). Furthermore, for a fixed n, x_i <= (n+1i)*(A000058(i1)1).  Max Alekseyev, Oct 11 2012


REFERENCES

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).


LINKS

M. K. Azarian, Diophantine Pair, Problem B881, Fibonacci Quarterly, Vol. 37, No. 3, August 1999, pp. 277278; Solution to Problem B881, Fibonacci Quarterly, Vol. 38, No. 2, May 2000, pp. 183184.


FORMULA



EXAMPLE

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.


CROSSREFS



KEYWORD

nonn,nice,hard,more


AUTHOR



EXTENSIONS

a(8) from John Dethridge (jcd(AT)ms.unimelb.edu.au), Jan 08 2004


STATUS

approved



