Problem
NT-B2-M10-P001 Compute the Functions
#1
★★☆☆☆ Level 2 of 5
Compute \(\tau(540)\), \(\sigma(540)\), \(\varphi(540)\).
Start by factoring \(540\).
\(540=2^2\cdot 3^3\cdot 5\). Therefore \(\tau(540)=3\cdot 4\cdot 2=24\). Also \(\sigma(540)=(1+2+4)(1+3+9+27)(1+5)=7\cdot 40\cdot 6=1680\). Finally, \(\varphi(540)=540\cdot\frac12\cdot\frac23\cdot\frac45=144\).
Basic practice with the formulas.