一道DS题,(2)的含义是什么?

Is the integer n odd?
(1)     n is divisible by 3.
(2)     2n is divisible by twice as many positive integers as n

B

这题大家选什么??对2的理解又是什么呢?

(1) By checking n=6, n=9, it's easy to know the premise is inconclusive.

(2) Assume n has factors 1,a1,a2,...n, then 2n must have factors 1,a1,a2...n and 2,2a1,2a2...2n.

Since 2n has twice as many factors as n, there should be no overlapping between 1,a1,a2..n and 2,2a1,2a2,...2n.

In another word, for any ai among 1,a1,..n, 2ai is not a factor of n. Therefore n must be an odd number.