and as usual co(n) is the number of distinct prime factors of n, f2(n) is the total number of prime factors of n, f II n means that p~ (p prime) exactly divides n. It was shown in [1] that, for each fixed natural number m, there exist computable constants el, e z, ..., era, fa,f2 ..... fro, 0 2). These questions were considered in a general setting by De Koninck and Mercier [2], where under suitable conditions asymptotic relations of the form (1.3) Y~ f(P(n)) = (1 + o(1)) Z f(n) (x ~co)

In this paper, we study maximal, minimal, normal and average order of the function n f(n) = II njgcd(n,k!) k=O

/pdf/on-the-number-of-polynomial-maps-into-z-n-4q0fj5o5po.pdf

The average prime divisor of an integer in short intervals

On the number of polynomial maps into Z_n

Three basic principles.- The large sieve.- Arithmetic formulations of the large sieve.- A weighted sieve and its application.- A lower bound of Roth.- Classical mean value theorems.- New mean value theorems.- Large moduli theorems.- Further results and conjectures concerning mean and large moduli.- Mean moduli of L-functions.- Zero-free regions and the proliferation of zeros.- Distribution of zeros of L-functions.- Least character non-residues and arg L(12+it, x).- The prime number theorems of Hoheisel and Selberg.- The bombieri - Vinogradov theorem.- A lemma in additive prime number theory.- The mean value theorem of Barban.

Topics in Multiplicative Number Theory

The Riemann zeta-function

result

On the difference between consecutive primes

https://link.springer.com/content/pdf/10.1007/BF01193609.pdf

The average prime divisor of an integer in short intervals

Citations

On the number of polynomial maps into Z_n

References

Topics in Multiplicative Number Theory

The Riemann zeta-function

On the difference between consecutive primes

The distribution of the average prime divisor of an integer

On sums of large differences between consecutive primes

Related Papers (5)

On f(n) modulo Ω( n) and ω( n) when f is a polynomial

Prime powers dividing products of consecutive integer values of $x^{2^n}+1$

The Rational Number n/p as a sum of two unit fractions

Integer-valued polynomials on prime numbers and logarithm power expansion

The number of large prime divisors of consecutive integers