On square values of the product of the Euler totient and sum of divisors functions
If n is a positive integer such that ϕ(n)σ(n) = m² for some positive integer m, then m ≤ n. We put m = n-a and we study the positive integers a arising in this way.
Restricted divisor sums
The average order of the Dirichlet series of the gcd-sum function.
Characterizing the sum of two cubes.
The gcd-sum function.
Asymptotic order of the square-free part of .
Divisibility by 3 of even multiperfect numbers of abundancy 3 and 4.
On the subsequence of primes having prime subscripts.
On the number of solutions of exponential congruences
Some divisibility properties of binomial coefficients and the converse of Wolstenholme's theorem.
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