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

1,1

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.

Links

Table of n, a(n) for n=1..65.

G. Martin, Denser Egyptian fractions, Acta Arith. 95 (2000), no. 3, 231-260.

G. Martin, Dense Egyptian fractions, Talk at the AMS Spring Central Sectional Meeting, University of Illinois at Urbana-Champaign, March 27, 2009.

Example

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.

Crossrefs

Sequence in context: A060683 A129511 A174905 * A368087 A191849 A055019

Adjacent sequences: A260399 A260400 A260401 * A260403 A260404 A260405

Keyword

nonn

Author

M. F. Hasler, Jul 24 2015

Status

approved