Question

Find φ (1600), σ (1600).

Answer 1

$1600=16\times4\times25=2^6\times5^2$

$\phi(2^6\times5^2)=\phi(2^6)\times\phi(5^2)=(2^6-2^5)\times(5^2-5^1)=\boxed{640}$

$\sigma(2^6\times5^2)=\sigma(2^6)\times\sigma(5^2)=\frac{2^{6+1}-1}{2-1}\times\frac{5^{2+1}-1}{5-1}=\frac{127}{1}\times\frac{124}{4}=\boxed{3937}$