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 A006585 Egyptian fractions: number of solutions to 1 = 1/x_1 + ... + 1/x_n in positive integers x_1 < ... < x_n. (Formerly M4281) 10
 1, 0, 1, 6, 72, 2320, 245765, 151182379 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 COMMENTS All denominators in the expansion 1 = 1/x_1 + ... + 1/x_n are bounded by A000058(n-1), i.e., 0 < x_1 < ... < x_n < A000058(n-1). Furthermore, for a fixed n, x_i <= (n+1-i)*(A000058(i-1)-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 B-881, Fibonacci Quarterly, Vol. 37, No. 3, August 1999, pp. 277-278; Solution to Problem B-881, Fibonacci Quarterly, Vol. 38, No. 2, May 2000, pp. 183-184. 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, 95:1-2 (2014), 277-281. T. D. Browning, C. Elsholtz, The number of representations of rationals as a sum of unit fractions, Illinois J. Math. 55:2 (2011), 685-696. 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

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Last modified June 3 17:31 EDT 2023. Contains 363116 sequences. (Running on oeis4.)