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Acta Arithmetica

Acta Arithmetica

Acta Arithmetica

Acta Arithmetica

Acta Arithmetica

The Continuity of the Limiting Distribution of a Function of Two Additive Functions.

Mathematische Zeitschrift

Normal numbers and the middle prime factor of an integer

Colloquium Mathematicae

Let pₘ(n) stand for the middle prime factor of the integer n ≥ 2. We first establish that the size of log pₘ(n) is close to √(log n) for almost all n. We then show how one can use the successive values of pₘ(n) to generate a normal number in any given base D ≥ 2. Finally, we study the behavior of exponential sums involving the middle prime factor function.

Shifted values of the largest prime factor function and its average value in short intervals

Colloquium Mathematicae

We obtain estimates for the average value of the largest prime factor P(n) in short intervals [x,x+y] and of h(P(n)+1), where h is a complex-valued additive function or multiplicative function satisfying certain conditions. Letting ${s}_{q}\left(n\right)$ stand for the sum of the digits of n in base q ≥ 2, we show that if α is an irrational number, then the sequence ${\left(\alpha {s}_{q}\left(P\left(n\right)\right)\right)}_{n\in ℕ}$ is uniformly distributed modulo 1.

On the number of prime divisors of the iterates of the Carmichael function.

Mathematica Pannonica

Square-free values of the Carmichael function.

Mathematica Pannonica

A remark on a paper written by J. M. De Koninck and A. Ivić.

Mathematica Pannonica

On the function $\zeta \left(S\right)\zeta \left(S-A\right)\cdots \zeta \left(S-RA\right)=\sum \frac{{\sigma }_{A,R+1}\left(N\right)}{{N}^{S}}$.

Mathematica Pannonica

On asymptotically correlated $q$-multiplicative functions.

Mathematica Pannonica

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