HMMT 十一月 2008 · 冲刺赛 · 第 36 题
HMMT November 2008 — Guts Round — Problem 36
题目详情
- [ 25 ] How many numbers less than 1 , 000 , 000 are the product of exactly 2 distinct primes? You will N receive b 25 − 50 · | − 1 |c points, if you submit N and the correct answer is A . A . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
解析
- [ 25 ] How many numbers less than 1 , 000 , 000 are the product of exactly 2 distinct primes? You will N receive b 25 − 50 · | − 1 |c points, if you submit N and the correct answer is A . A Answer: 209867 While it is difficult to compute this answer without writing a program or using a calculator, it can be approximated using the fact that the number of primes less than a positive integer n n is about . log n 7