

A006585


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


8




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
If on the other hand, x_k need not be unique, see A002966.  Robert G. Wilson v, Jul 17 2013


REFERENCES

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


LINKS

Table of n, a(n) for n=1..8.
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.
M. Le Brun, Email to N. J. A. Sloane, Jul 1991
S. V. Konyagin, Double exponential lower bound for the number of representations of unity by Egyptian fractions. Mathematical Notes, 95:12 (2014), 277281.
T. D. Browning, C. Elsholtz, The number of representations of rationals as a sum of unit fractions, Illinois J. Math. 55:2 (2011), 685696.
Index entries for sequences related to Egyptian fractions


FORMULA

a(n) = A280520(n,1).


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

Cf. A000058, A002966, A002967, A280518.
Sequence in context: A259212 A279234 A132878 * A166472 A182917 A328814
Adjacent sequences: A006582 A006583 A006584 * A006586 A006587 A006588


KEYWORD

nonn,nice,hard,more


AUTHOR

N. J. A. Sloane.


EXTENSIONS

a(1)a(7) are confirmed by Jud McCranie, Dec 11 1999
a(8) from John Dethridge (jcd(AT)ms.unimelb.edu.au), Jan 08 2004


STATUS

approved



