Kidnapping

发布时间: 2018年10月7日 10:50   最后更新: 2018年10月15日 09:31   时间限制: 2000ms   内存限制: 512M

How many non-empty sets of positive integers exist such that their greatest common divisor is $1$, while their least common multiple is $m$?

The first line contains an integer $T$ - the number of cases.($T \le 200$)
For each case, one line contains a single integer $m$.($1 \le m \le 10 ^{18}$)

For each case, output a single integer - the answer modulo $998,244,353$.

复制
2
6
100
7
322

In the first example test case, all suitable sets are $\lbrace 1, 6 \rbrace$, $\lbrace 2, 3 \rbrace$, $\lbrace 1, 2, 3 \rbrace$, $\lbrace 1, 2, 6 \rbrace$, $\lbrace 1, 3, 6 \rbrace$, $\lbrace 2, 3, 6 \rbrace$ and $\lbrace 1, 2, 3, 6 \rbrace$,

math

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