Add to ORKGWe prove that the only solutions to the equation σ(n)=2φ(n) with at most three distinct prime factors are 3, 35 and 1045. Moreover, there exist at most a finite number of solutions to σ(n)=2φ(n) with Ω(n)≤ k, and there are at most 22k+k-k squarefree solutions to φ (n)|σ(n) if ω(n)=k. Lastly the number of solutions to φ(n)|φ(n) as x→∞ is O(x exp(-½√log x))
From the Washington University Senior Honors Thesis Abstracts (WUSHTA), 2017. Published by the Offic...
Abstract. We study the solutions of the equation φ(Cm)/φ(Cn) = r, where r is a fixed rational numbe...
We study the sum [equation omitted for formating reasons] of consecutive iterations of the Euler fun...
We find the form of all solutions to φ(n) |σ(n) with three or fewer prime factors, except when the q...
We find the form of all solutions to ø(n) | σ(n) with three or fewer prime factors, except when the ...
We prove that the only solutions to the equation σ(n)=2φ(n) with at most three distinct prime factor...
ABSTRACT. We show that the equation φ(a) = σ(b) has infinitely many solutions, where φ is Euler’s t...
We study integers n > 1 satisfying the relation σ(n) = γ(n) ² , where σ(n) and γ(n) are the sum of d...
Let φ denote the Euler function. For a fixed integer k ≠ 0, we study positive integers n for which t...
We study integers n > 1 satisfying the relation σ(n) = γ(n)², where σ(n) and γ(n) are the sum of div...
Let denotes the sum of the positive divisors of the positive integer and be the Euler’s totient f...
AbstractLet N be sufficiently large odd integer. It is proved that the equation N=n1+n2+n3 has solut...
For any positive integer k let φ(k), σ(k), and τ(k) be the Euler function of k, the divisor sum func...
Let ϕ denote Euler’s totient function. It is shown that if r ≥ 2 there exist only finitely many posi...
AbstractThe expressions ϕ(n)+σ(n)−3n and ϕ(n)+σ(n)−4n are unusual among linear combinations of arith...
From the Washington University Senior Honors Thesis Abstracts (WUSHTA), 2017. Published by the Offic...
Abstract. We study the solutions of the equation φ(Cm)/φ(Cn) = r, where r is a fixed rational numbe...
We study the sum [equation omitted for formating reasons] of consecutive iterations of the Euler fun...
We find the form of all solutions to φ(n) |σ(n) with three or fewer prime factors, except when the q...
We find the form of all solutions to ø(n) | σ(n) with three or fewer prime factors, except when the ...
We prove that the only solutions to the equation σ(n)=2φ(n) with at most three distinct prime factor...
ABSTRACT. We show that the equation φ(a) = σ(b) has infinitely many solutions, where φ is Euler’s t...
We study integers n > 1 satisfying the relation σ(n) = γ(n) ² , where σ(n) and γ(n) are the sum of d...
Let φ denote the Euler function. For a fixed integer k ≠ 0, we study positive integers n for which t...
We study integers n > 1 satisfying the relation σ(n) = γ(n)², where σ(n) and γ(n) are the sum of div...
Let denotes the sum of the positive divisors of the positive integer and be the Euler’s totient f...
AbstractLet N be sufficiently large odd integer. It is proved that the equation N=n1+n2+n3 has solut...
For any positive integer k let φ(k), σ(k), and τ(k) be the Euler function of k, the divisor sum func...
Let ϕ denote Euler’s totient function. It is shown that if r ≥ 2 there exist only finitely many posi...
AbstractThe expressions ϕ(n)+σ(n)−3n and ϕ(n)+σ(n)−4n are unusual among linear combinations of arith...
From the Washington University Senior Honors Thesis Abstracts (WUSHTA), 2017. Published by the Offic...
Abstract. We study the solutions of the equation φ(Cm)/φ(Cn) = r, where r is a fixed rational numbe...
We study the sum [equation omitted for formating reasons] of consecutive iterations of the Euler fun...