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A sequence is called $k$ -automatic if the $n$ ’th term in the sequence can be generated by a finite state machine, reading $n$ in base $k$ as input. We show that for many multiplicative functions, the sequence ${(f (n) mod v)}_{n \geq 1}$ is not $k$ -automatic. Among these multiplicative functions are $γ_{m} (n), σ_{m} (n), μ (n)$ et $φ (n)$ .

Multiplicative functions over short segments

Olivier Bordellès (2013)

Acta Arithmetica

Multiplicative functions satisfying the equation $f (m^{2} + n^{2}) = f (m^{2}) + f (n^{2})$

Pham Van Chung (1996)

Mathematica Slovaca

Multiplicative functions with difference tending to zero

Eduard Wirsing, Don Zagier (2001)

Acta Arithmetica

Mycielski-Sierpiński conjecture and Korec-Znám result

Marc A. Berger, Alexander Felzenbaum, Aviezri S. Fraenkel (1988)

Colloquium Mathematicae

Několik kapitol z nauky o číslech

Emil Schönbaum (1905)

Časopis pro pěstování mathematiky a fysiky

Neuere Untersuchungen über die Jacobsthal-Funktion g(n).

H.-J. Kanold (1977)

Monatshefte für Mathematik

New Inversion Properties of ... and ...*.

D. Suryanarayana (1971)

Elemente der Mathematik

Nonaliquots and Robbins numbers

William D. Banks, Florian Luca (2005)

Colloquium Mathematicae

Let φ(·) and σ(·) denote the Euler function and the sum of divisors function, respectively. We give a lower bound for the number of m ≤ x for which the equation m = σ(n) - n has no solution. We also show that the set of positive integers m not of the form (p-1)/2 - φ(p-1) for some prime number p has a positive lower asymptotic density.

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Multiplicative $B$ -product and its properties.

Multiplicative even functions (mod r). I Structural properties.

Multiplicative even functions (mod r). II Identities involving Ramanujan sums.

Multiplicative functions and $k$ -automatic sequences

Multiplicative functions over short segments

Multiplicative functions satisfying the equation $f (m^{2} + n^{2}) = f (m^{2}) + f (n^{2})$

Multiplicative functions with difference tending to zero

Mycielski-Sierpiński conjecture and Korec-Znám result

Několik kapitol z nauky o číslech

Neuere Untersuchungen über die Jacobsthal-Funktion g(n).

New Inversion Properties of ... and ...*.

Nonaliquots and Robbins numbers

Note on a congruence involving products of binomial coefficients.

Note on multiplicative functions satisfying congruence property. II.

Note on perfect and multiply perfect numbers

Note sur les diviseurs d'un nombre entier

Notes on generalized Dedekind sums

Notes on power LCM matrices

Nouveau théorème concernant la fonction numérique $F (k)$ .

O číselnoteoretickej funkcii $d (n)$

Currently displaying 181 – 200 of 487