Continuity module of the distribution of additive functions related to the largest prime factors of integers

1990 ◽  
Vol 55 (5) ◽  
pp. 450-461 ◽  
Author(s):  
J. M. De Koninck ◽  
I. Kátai ◽  
A. Mercier
Keyword(s):  
Additive Functions ◽  
Continuity Module ◽  
Prime Factors

On the prime factors of the iterates of the Ramanujan τ–function

2020 ◽  
Vol 63 (4) ◽  
pp. 1031-1047
Author(s):  
Florian Luca ◽  
Sibusiso Mabaso ◽  
Pantelimon Stănică
Keyword(s):  
Positive Integer ◽  
Prime Factors

AbstractIn this paper, for a positive integer n ≥ 1, we look at the size and prime factors of the iterates of the Ramanujan τ function applied to n.

On triplets with descending largest prime factors

2001 ◽  
Vol 38 (1-4) ◽  
pp. 45-50 ◽  
Author(s):  
A. Balog
Keyword(s):  
Prime Factor ◽  
Prime Factors ◽  
Consecutive Integers

For an integer n≯1 letP(n) be the largest prime factor of n. We prove that there are infinitely many triplets of consecutive integers with descending largest prime factors, that is P(n - 1) ≯P(n)≯P(n+1) occurs for infinitely many integers n.

scholarly journals On integers free of large prime factors

1986 ◽  
Vol 296 (1) ◽  
pp. 265-265 ◽  
Author(s):  
Adolf Hildebrand ◽  
G{érald Tenenbaum
Keyword(s):  
Prime Factors

scholarly journals On $p$ and $q$-Additive Functions

1999 ◽  
Vol 22 (1) ◽  
pp. 83-97 ◽  
Author(s):  
Yoshihisa UCHIDA
Keyword(s):  
Additive Functions
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