Results 221 to 229 of about 542,394 (229)

STRONGLY -ADDITIVE FUNCTIONS AND DISTRIBUTIONAL PROPERTIES OF THE LARGEST PRIME FACTOR

Bulletin of the Australian Mathematical Society, 2015
Let $P(n)$ denote the largest prime factor of an integer $n\geq 2$. In this paper, we study the distribution of the sequence $\{f(P(n)):n\geq 1\}$ over the set of congruence classes modulo an integer $b\geq 2$, where $f$ is a strongly $q$-additive integer-valued function (that is, $f(aq^{j}+b)=f(a)+f(b),$ with $(a,b,j)\in \mathbb{N}^{3}$, $0\leq b<q^
Amri, M., Mkaouar, M., Wannes, W.
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On the largest prime factors of consecutive integers

Monatshefte für Mathematik
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Xiaodong Lü, Zhiwei Wang
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The Largest Prime Factor of Integers in the Short Interval

2002
In this report, the progress on the largest prime factor of integers in the short interval of two kinds is introduced.
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On the largest prime factors of consecutive square-free integers

Acta Arithmetica
For an integer n>1, let P+(n) be the largest prime factor of n. Following a celebrated conjecture of Erdős and Turán in the 1930s, Erdős and Pomerance proved in 1978 that lim infx→∞|{n≤x:P+(n+1)>P+(n)}|x>0. In this article, their result is extended to lim infx→∞|{n≤x:P+(n+1)>P+(n),μ2(n)=μ2(n+1)=1}|x>0.
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Exponential sums involving the largest prime factor function

Acta Arithmetica, 2011
Jean-Marie De Koninck, Imre Kátai
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On the largest prime factor of p + a

Mathematika, 1973
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On the largest prime factor of a Mersenne number

2004
Leo Murata, Carl Pomerance
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Sum of reciprocals of the largest prime factor of an integer

Archiv der Mathematik, 1981
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Largest prime factor of the product of k consecutive integers

1975
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