2. 外语
  3. How many integers between 99 and 365 are there such that they have 3 divisors?

How many integers between 99 and 365 are there such that they have 3 divisors?

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问题 How many integers between 99 and 365 are there such that they have 3 divisors?
选项 A、2
B、4
C、6
D、8
E、10
答案B
解析 据因数个数公式n=(a1+1)(a2+1)…(an+1)=3，可知a2=2，即将所求整数做质因数分解后，只有一个质因数，且该整数为此质因数的平方。于是本题变为：99到365之间有多少整数是质数的平方?99后面的完全平方数是100=102；365前面的完全平方数是361=192；那么10到19之间有质数11、13、1 7、19这4个，即99到365之间有4个质数的平方。答案为B选项。
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