Additive functions and their actions on certain elementary functions
نویسندگان
چکیده
منابع مشابه
On Certain Large Additive Functions
pα||n α. As usual p will denote primes, pα||n means that p divides n but p does not, and a function f(n) is additive if f(mn) = f(m)+f(n) whenever (m,n) = 1. From the pioneering works of Alladi and Erdős [1]-[2], P. Erdős’s perspicacity and insight have been one of the main driving forces in the research that brought on many results on summatory functions of large additive functions and P (n). ...
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1 . Introduction and statement of results Let (3(n) = Y_, In p and B (n) = y_p . j jn ap denote the sum of distinct prime divisors of n and the sum of all prime divisors of n respectively . Both (3(n) and B(n) are additive functions which are in a certain sense large (the average order of B(n) is Tr'n/(6log n), [1]) . For a fixed integer m the number of solutions of B(n) = m, is the number of p...
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ژورنال
عنوان ژورنال: Mathematical Inequalities & Applications
سال: 2015
ISSN: 1331-4343
DOI: 10.7153/mia-18-80