Theorem 2. for each k \geq 2 and every fixed A < e1/k we have \tauk(n) > (log n)A infinitely often.
The last proven result involves the divisors of two integers. We say that two integers m and n interlock if every pair of divisors of n are separated by a divisor of m, and conversely (except for 1 and the smallest prime factor ofmn). An integer n is said to be separable if there exists an integer m such that m and n interlock, and let A(x) be the number of separable n \leq x. It is proven: Theorem 4. For every fixed c' > 0 and sufficiently large x we have
Classif.: * 11N37 Asymptotic results on arithmetic functions
Keywords: asymptotic results; divisor function
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