On the Number of Integers Representable as Sums of Unit Fractions, III
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, logn+γ− π 2 3 +o(1) (log 2n) 2 logn ⩽∣N(n)∣ , which improves the lower bound given by Croot.
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| Veröffentlicht in: | Journal of number theory 2002-10, Vol.96 (2), p.351-372 |
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| 1. Verfasser: | |
| Format: | Artikel |
| Sprache: | eng |
| Online-Zugang: | Volltext |
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| Zusammenfassung: | 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,
logn+γ−
π
2
3
+o(1)
(log
2n)
2
logn
⩽∣N(n)∣
, which improves the lower bound given by Croot. |
|---|---|
| ISSN: | 0022-314X 1096-1658 |
| DOI: | 10.1006/jnth.2002.2797 |