APS2 - Amazing Prime Sequence (hard)
This problem is a harder version of APS.
Let $f(n)$ be the smallest prime factor of $n$. For example, $f(2) = 2,\ f(4) = 2$ and $f(35) = 5$.
The sequence $S(n)$ is defined for all positive integers as follows:
- $S(1) = 0$
- $S(n) = S(n-1) + f(n)$ (if $n \ge 2$)
Given $N$, find $S(N)$ modulo $2^{64}$.
Input
First line contains $T$ ($1 \le T \le 10000$), the number of test cases.
Each of the next $T$ lines contains a single integer $N$. ($1 \le N \le 1234567891011$)
Output
For each integer $N$, output a single line containing $S(N)$ modulo $2^{64}$.
Example
Input
5
1
4
100
1000000
1000000000000
Output
0
7
1257
37568404989
7294954823202325427
Explanation for Input
- $S(4) = 2 + 3 + 2 = 7$
- $S(10^{12}) = 18435592284459044389811 \equiv 7294954823202325427 \pmod{2^{64}}$
Information
There are 6 Input files.
- Input #0: $1 \le T \le 10000$, $1 \le N \le 10000$, TL = 1s.
- Input #1: $1 \le T \le 1000$, $1 \le N \le 10^{8}$, TL = 20s.
- Input #2: $1 \le T \le 200$, $1 \le N \le 10^{9}$, TL = 20s.
- Input #3: $1 \le T \le 40$, $1 \le N \le 10^{10}$, TL = 20s.
- Input #4: $1 \le T \le 7$, $1 \le N \le 10^{11}$, TL = 20s.
- Input #5: $T = 1$, $1 \le N \le 1234567891011$, TL = 20s.
My solution runs in 5.36 sec. (total time)
Source Limit is 8 KB.
hide comments
[Rampage] Blue.Mary:
2016-04-15 05:18:17
The source limit and time limit are both reasonable (twice of my ugly code's source length and running time) for solving this problem. Thanks to min_25 for setting those constraints carefully. Last edit: 2016-04-15 05:19:29 |
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abdou_93:
2015-01-28 08:40:19
not (hard).for more sense (impossible) |
Added by: | Min_25 |
Date: | 2014-06-05 |
Time limit: | 1s-20s |
Source limit: | 8192B |
Memory limit: | 1536MB |
Cluster: | Cube (Intel G860) |
Languages: | All except: ASM64 GOSU |
Resource: | APS |