HMMT 二月 2000 · 代数 · 第 7 题
HMMT February 2000 — Algebra — Problem 7
题目详情
英文原题
- A number n is alled m ultipli ativ ely p erfe t if the pro du t of all the p ositiv e divisorsof n is n . Determine the number of p ositiv e m ultipli ativ ely p erfe t n um b ers less than 2
解析
英文解析
- All m ultipli ativ ely p erfe t n um b ers have exa tly 4 distin t p ositiv e divisors, or 1. So,
we m ust lo ok for n um b ers that are eithera pro du t of t w o distin t primes 1
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