The "prime sum" of an integer n greater than 1 is the sum of all the prime factors of n, including repetitions. For example, the prime sum of 12 is 7, since 12 = 2 x 2 x 3 and 2 + 2 + 3 = 7. For which of the following integers is the prime sum greater than 35 ?

440

512

620

700

750

##### 考题讲解

440=2*2*2*5*11， the prime sum 就是 2+2+2+5+11=22,不大于 35；

512=~$2^9$~；  the prime sum 就 是 2*9=18, 不 大 于 35；

620=2*2*5*31, the prime sum=2+2+5+31=40, 大于 35. 答案；

700=2*2*5*5*7    the prime sum=2+2+5+5+7=21,不大于 35.

750=2*3*5*5*5，the prime sum=2+3+5+5+5=20,不大于 35.