Smoj 1069 antiprime (http: // 218.5.241.13: 8060/OJ/showproblem. jsp? PID = 1069)

I. Definition: If a number M has more than any natural number smaller than m, this number is called antiprime. For example, 1, 2, 4, 6, 12, and 24.

2. theorem set m = 2 ^ T1 × 3 ^ T2 × ...... * P ^ TK (where p is the prime number of K) is the antiprime number, then T1 must be ≥t2 ≥t3 ≥ ...... ≥ TK ≥ 0.

Use the reverse certificate. (Omitted)

Iii. Analysis

1. Since n can reach 2*10 ^ 9, it takes more time to use enumeration.

2. When n = 2*10 ^ 9, there are only 1456 antiprime instances. Therefore, you can search and store all such numbers, and record the approximate number of each number. Sort them from small to large, and then determine the antiprime numbers one by one, and take the maximum value. For example, if n = 15, the number of the conditions is 1, 2, 4, 6, and 12, and the number of the approximate numbers is 1, 2, 3, 4, 4, and 6, respectively, therefore, the number of antiprime values not greater than 15 is 1, 2, 4, 6, and 12, and the maximum value is 12.

4. Because 2 ^ 31 is close to 2*10 ^ 9, the index of 2 ranges from 31 to 30 ...... Search down. Use the Backtracking Method.