On locally repeated values of certain arithmetic functions. III
نویسندگان
چکیده
منابع مشابه
On Locally Repeated Values of Certain Arithmetic Functions, IV
Let ω(n) denote the number of prime divisors of n and letÄ(n) denote the number of prime power divisors of n. We obtain upper bounds for the lengths of the longest intervals below x whereω(n), respectivelyÄ(n), remains constant. Similarly we consider the corresponding problems where the numbers ω(n), respectivelyÄ(n), are required to be all different on an interval. We show that the number of s...
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which is nearly 1 if K is large . Thus if n and n+1 both satisfy (1 .3) and if we view v(n) and v(n+l) as "independent events", then the "probability" that (L2) holds should be at least (2K Vlog log n)-1 . Summing these probabilities would then give order of magnitude x1f log log x solutions n of (1 .2) with n-x, thus supporting the conjecture. A refinement of this heuristic argument even sugge...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1987
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-1987-0897061-6