A260402 Numbers which cannot be the largest denominator of an Egyptian fraction for 1.

2, 3, 4, 5, 7, 8, 9, 10, 11, 13, 14, 16, 17, 19, 21, 22, 23, 25, 26, 27, 29, 31, 32, 34, 37, 38, 39, 41, 43, 44, 46, 47, 49, 50, 51, 53, 57, 58, 59, 61, 62, 64, 67, 68, 69, 71, 73, 74, 79, 81, 82, 83, 86, 87, 89, 92, 93, 94, 97, 98, 101, 103, 106, 107, 109

Offset: 1

Author

M. F. Hasler, Jul 24 2015

Keywords

• nonn

Comments

Complement of A092671.

Contains at all primes and prime powers (A000961).

Martin studies the asymptotic behavior of this sequence: the order of magnitude of its counting function (number of elements below x) is x log log x / log x.

Examples

			10 is in this sequence because any Egyptian fraction with 1/10 as its term with largest denominator either contains 1/5 as well or not; either way, the resulting sum will have a factor 5 in its denominator (any other term will contribute a multiple of 5 to the numerator of the sum), hence cannot equal 1.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..5000
• Greg Martin, Denser Egyptian fractions, Acta Arith. 95 (2000), no. 3, 231-260.
• Greg Martin, Dense Egyptian fractions, Talk at the AMS Spring Central Sectional Meeting, University of Illinois at Urbana-Champaign, March 27, 2009.