On integers n with for .
On integers with a special divisibility property
In this note, we study those positive integers which are divisible by , where is the Carmichael function.
On integers with many small prime factors
On invariants related to non-unique factorizations in block monoids and rings of algebraic integers
On irregularities in the graph of generalized divisor functions
On isolated, respectively consecutive large values of arithmetic functions
On Jacobsthal's g(n)-Function.
On linear forms in the logarithms of algebraic numbers
On Linnik's constant.
On Linnik's constant
On Mellin-Ramanujan expansions
On Mirsky's generalisation of a problem of Evelyn-Linfoot and Page in additive theory of numbers.
On multiplicative magic squares.
On multiplicatively perfect numbers.
On oscillations in the additive divisor problem, 1
On periodic mod p sequences and G-functions (On a conjecture of Ruzsa).
On polynomials that are sums of two cubes.
It is proved that, if F(x) be a cubic polynomial with integral coefficients having the property that F(n) is equal to a sum of two positive integral cubes for all sufficiently large integers n, then F(x) is identically the sum of two cubes of linear polynomials with integer coefficients that are positive for sufficiently large x. A similar result is proved in the case where F(n) is merely assumed to be a sum of two integral cubes of either sign. It is deduced that analogous propositions are true...
On Popov's explicit formula and the Davenport expansion
We shall establish an explicit formula for the Davenport series in terms of trivial zeros of the Riemann zeta-function, where by the Davenport series we mean an infinite series involving a PNT (Prime Number Theorem) related to arithmetic function with the periodic Bernoulli polynomial weight and PNT arithmetic functions include the von Mangoldt function, Möbius function and Liouville function, etc. The Riesz sum of order or gives the well-known explicit formula for respectively the partial...
On positive integers with a certain nondivisibility property.
On power-free numbers and polynomials. I.