Answers

2015-05-05T09:58:54+05:30
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}
1 5 1
basically φ(n) gives you the number of positive coprime integers less than or equal to n
and it is a multiplicative function, so φ(a*b) = φ(a)*φ(b) whenever gcd(a,b)=1
can u write the formula?
φ(p^k) = p^k - p^(k-1) where p is prime
got it.thanks