Problem
NT-B1-M09-P023 When \( au(2n)=2 au(n)\)
#23
★★★★☆ Level 4 of 5
Find all positive integers \(n\) such that \(\tau(2n)=2\tau(n)\).
Let \(n=2^a m\), where \(m\) is odd.
Let \(n=2^a m\), with \(m\) odd. Then \(\tau(n)=(a+1)\tau(m)\), while \(\tau(2n)=(a+2)\tau(m)\). The condition gives \(a+2=2(a+1)\), hence \(a=0\). Thus \(n\) must be odd. All odd \(n\) work.
Good parametric problem on the power of two.