On the function
On the index of an odd perfect number
Suppose that N is an odd perfect number and is a prime power with . Define the index . We prove that m cannot take the form , where u is a positive integer and 2u+1 is composite. We also prove that, if q is the Euler prime, then m cannot take any of the 30 forms q₁, q₁², q₁³, q₁⁴, q₁⁵, q₁⁶, q₁⁷, q₁⁸, q₁q₂, q₁²q₂, q₁³q₂, q₁⁴ q₂, q₁⁵q₂, q₁²q₂², q₁³q₂², q₁⁴q₂², q₁q₂q₃, q₁²q₂q₃, q₁³q₂q₃, q₁⁴q₂q₃, q₁²q₂²q₃, q₁²q₂²q₃², q₁q₂q₃q₄, q₁²q₂q₃q₄, q₁³q₂q₃q₄, q₁²q₂²q₃q₄, q₁q₂q₃q₄q₅, q₁²q₂q₃q₄q₅, q₁q₂q₃q₄q₅q₆,...
On the Integers Relatively Prime to n and a Number-Theoretic Function Considered by Jacobsthal.
On the norm of GCD and related matrices.
On the maximum row and column sum norm of GCD and related matrices.
On the Möbius function.
On the Möbius sum function
On the multiplicative order of modulo .
On the nth Powers of the Primitive Nth roots of Unity
On the number of distinct values of Euler's φ-function
On the number of elements with maximal order in the multiplicative group modulo n
On the number of nonquadratic residues which are not primitive roots
We show that there exist infinitely many positive integers r not of the form (p-1)/2 - ϕ(p-1), thus providing an affirmative answer to a question of Neville Robbins.
On the number of representations of a positive integer by certain quadratic forms
For natural numbers a,b and positive integer n, let R(a,b;n) denote the number of representations of n in the form . Lomadze discovered a formula for R(6,0;n). Explicit formulas for R(1,5;n), R(2,4;n), R(3,3;n), R(4,2;n) and R(5,1;n) are determined in this paper by using the (p;k)-parametrization of theta functions due to Alaca, Alaca and Williams.
On the number of solutions of f(n) = a for additive functions
On the number of subsets of relatively prime to and asymptotic estimates.
On the number of subsets relatively prime to an integer.
On the problem of odd h-fold perfect numbers
On the product of divisors of a positive integer
On the product of divisors of and of .
On the properties of oscillation and almost periodicity of certain convolutions