LCMSUM  LCM Sum
Given n, calculate the sum LCM(1,n) + LCM(2,n) + .. + LCM(n,n), where LCM(i,n) denotes the Least Common Multiple of the integers i and n.
Input
The first line contains T the number of test cases. Each of the next T lines contain an integer n.
Output
Output T lines, one for each test case, containing the required sum.
Example
Sample Input: 3 1 2 5 Sample Output: 1 4 55
Constraints
1 <= T <= 300000
1 <= n <= 1000000
hide comments
DK...:
20180830 18:43:29
i got TL using pragma's, but AC without them...


uvshuvo:
20180629 01:30:42
Learned a lot about phi function nice math logic Thanks. Last edit: 20180629 01:34:23 

crackeree:
20180503 14:49:26
how alien i m. everyone is getting TLE .. and i m getting WA..


chetan4060:
20180101 09:51:18
nice math used:) 

epsilonalpha:
20171214 07:37:25
It's a must do NT problem.


shub120798:
20170927 08:51:33
really nice prblm.. precompute each and every thing to avoid tle;..


rohit9934:
20170630 13:09:54
I have got so many TLE's in this


da_201501181:
20170402 13:54:53
Learned a lot..!! Nice Question..!! 

rohan_c_23:
20161013 13:33:03
Wonderful mathematics!!


square1001:
20160723 13:36:06
I suggest this problem: LCM Rush(Japanese).

Added by:  Varun Jalan 
Date:  20100124 
Time limit:  0.527s 
Source limit:  50000B 
Memory limit:  1536MB 
Cluster:  Cube (Intel G860) 
Languages:  All except: PERL6 
Resource:  own problem used for Codechef Snackdown Onsite 