HMMT 二月 2000 · 代数 · 第 7 题
HMMT February 2000 — Algebra — Problem 7
题目详情
- A n um b er n is alled m ultipli ativ ely p erfe t if the pro du t of all the p ositiv e divisors 2 of n is n . Determine the n um b er of p ositiv e m ultipli ativ ely p erfe t n um b ers less than
解析
- All m ultipli ativ ely p erfe t n um b ers ha v e exa tly 4 distin t p ositiv e divisors, or 1. So, w e m ust lo ok for n um b ers that are either 1 a pro du t of t w o distin t primes a ub e of a prime Num b ers satisfying one of these onditions less than 100 are: 1, 6, 8, 10, 14, 15, 21, 22, 26, 27, 33, 34, 35, 38, 39, 46, 51, 55, 57, 58, 62, 65, 69, 74, 77, 82, 85, 86, 87, 91, 93, 94,
- There are 33 of these. 3