

A006585


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


12




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



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



