算术基本定理

• $a = p_1^{a_1}*p_2^{a_2}*...*p_k^{a_k}$
  $b = p_1^{b_1}*p_2^{b_2}*...*p_k^{b_k}$
  $gcd(a,b) = p_1^{min(a_1,b_1)}*p_2^{min(a_2,b_2)}*...p_k^{min(a_k,b_k)}$
  $lcm(a,b) = p_1^{max(a_1,b_1)}*p_2^{max(a_2,b_2)}*...p_k^{max(a_k,b_k)}$
• $n = p_1^{c_1}*p_2^{c_2}*...*p_k^{c_k}$
• 因子个数：
  ${\prod}_{i=1}^{k}(c_i+1)$
• 因子之和
  ${\prod}_{i=1}^{k}{\frac{p_i^{c_i+1}-1}{p_i-1}}$