Od Fermatových čísel ke geometrii
Odd perfect numbers
Odd perfect numbers are divisible by at least seven distinct primes
Odd perfect numbers of a special form
We show that there is an effectively computable upper bound of odd perfect numbers whose Euler factors are powers of fixed exponent.
Odometers and systems of numeration
On -tuples of twin practical numbers
Un intero positivo si dice pratico se ogni intero con può essere espresso come una somma di divisori distinti positivi di . In questo articolo è affrontato il problema dell'esistenza di infinite cinquine di numeri pratici della forma .
On a certain class of arithmetic functions
A homothetic arithmetic function of ratio is a function such that for every . Periodic arithmetic funtions are always homothetic, while the converse is not true in general. In this paper we study homothetic and periodic arithmetic functions. In particular we give an upper bound for the number of elements of in terms of the period and the ratio of .
On a class of arithmetic convolutions involving arbitrary sets of integers.
On a class of arithmetical functions connected with multiplicative functions.
On a class of multiplicative arithmetic functions.
On a class of -convolutions characterized by the identical equation
The identical equation for multiplicative functions established by R. Vaidyanathaswamy in the case of Dirichlet convolution in 1931 has been generalized to multiplicativity preserving -convolutions satisfying certain conditions (cf. [7]) which can be called as Lehmer-Narkiewicz convolutions for some reasons. In this paper we prove the converse.
On a compositeness test for .
On a congruence by János Bolyai, connected with pseudoprimes.
On a congruence for the number of finite marked topologies
On a congruence of Emma Lehmer related to Euler numbers
A congruence of Emma Lehmer (1938) for Euler numbers modulo p in terms of a certain sum of reciprocals of squares of integers was recently extended to prime power moduli by T. Cai et al. We generalize this further to arbitrary composite moduli n and characterize those n for which the sum in question vanishes modulo n (or modulo n/3 when 3|n). Primes for which play an important role, and we present some numerical results.
On a Conjecture of A. Ivić and W. Schwarz
On a conjecture of Bruckman.
On a conjecture of Dekking : The sum of digits of even numbers
Let and denote by the sum-of-digits function in base . For considerIn 1983, F. M. Dekking conjectured that this quantity is greater than and, respectively, less than for infinitely many , thereby claiming an absence of a drift (or Newman) phenomenon. In this paper we prove his conjecture.
On A Conjecture of Emma Lehmer.
On a conjecture of Erdös