### Abstract

Let N(n) be the set of all integers that can be expressed as a sum of reciprocals of distinct integers <n. Then we prove that for sufficiently large n, log n + γ - (_{3}/^{π2} + o(1)) log n (log n)/(log_{2} n)^{2} ≤ (n) , which improves the lower bound given by Croot.

Original language | English |
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Pages (from-to) | 351-372 |

Number of pages | 22 |

Journal | Journal of Number Theory |

Volume | 96 |

Issue number | 2 |

DOIs | |

Publication status | Published - 2002 Oct 1 |

Externally published | Yes |

### ASJC Scopus subject areas

- Algebra and Number Theory

### Cite this

*Journal of Number Theory*,

*96*(2), 351-372. https://doi.org/10.1016/S0022-314X(02)92797-6

**On the number of integers representable as sums of unit fractions, III.** / Yokota, Hisashi.

Research output: Contribution to journal › Article

*Journal of Number Theory*, vol. 96, no. 2, pp. 351-372. https://doi.org/10.1016/S0022-314X(02)92797-6

}

TY - JOUR

T1 - On the number of integers representable as sums of unit fractions, III

AU - Yokota, Hisashi

PY - 2002/10/1

Y1 - 2002/10/1

N2 - Let N(n) be the set of all integers that can be expressed as a sum of reciprocals of distinct integers 3/π2 + o(1)) log n (log n)/(log2 n)2 ≤ (n) , which improves the lower bound given by Croot.

AB - Let N(n) be the set of all integers that can be expressed as a sum of reciprocals of distinct integers 3/π2 + o(1)) log n (log n)/(log2 n)2 ≤ (n) , which improves the lower bound given by Croot.

UR - http://www.scopus.com/inward/record.url?scp=0036802669&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0036802669&partnerID=8YFLogxK

U2 - 10.1016/S0022-314X(02)92797-6

DO - 10.1016/S0022-314X(02)92797-6

M3 - Article

AN - SCOPUS:0036802669

VL - 96

SP - 351

EP - 372

JO - Journal of Number Theory

JF - Journal of Number Theory

SN - 0022-314X

IS - 2

ER -