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A260402 Numbers which cannot be the largest denominator of an Egyptian fraction for 1. 0
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 (list; graph; refs; listen; history; text; internal format)
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 * A191849 A055019 A261466

Adjacent sequences:  A260399 A260400 A260401 * A260403 A260404 A260405

KEYWORD

nonn

AUTHOR

M. F. Hasler, Jul 24 2015

STATUS

approved

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Last modified February 20 13:53 EST 2020. Contains 332077 sequences. (Running on oeis4.)