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Integers divisible by sums of powers of their prime factors

โœ Scribed by Jean-Marie De Koninck; Florian Luca

Publisher
Elsevier Science
Year
2008
Tongue
English
Weight
115 KB
Volume
128
Category
Article
ISSN
0022-314X

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โœฆ Synopsis

For each positive integer j , let ฮฒ j (n) := p|n p j . Given a fixed positive integer k, we show that there are infinitely many positive integers n having at least two distinct prime factors and such that ฮฒ j (n) | n for each j โˆˆ {1, 2, . . . , k}.

๐Ÿ“œ SIMILAR VOLUMES

On sums of three integers with a fixed n
On sums of three integers with a fixed number of prime factors
โœ Xianmeng Meng ๐Ÿ“‚ Article ๐Ÿ“… 2005 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 292 KB

Let N be sufficiently large odd integer. It is proved that the equation N = n 1 + n 2 + n 3 has solutions, where n i has a fixed number of prime factors, and an asymptotic formula holds for the number of representations.

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โœ Jianya Liu; Ming-Chit Liu ๐Ÿ“‚ Article ๐Ÿ“… 2000 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 185 KB

As an extension of the Linnik Gallagher results on the ``almost Goldbach'' problem, we prove that every large even integer is a sum of four squares of primes and 8330 powers of 2.