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
nitin12384: 2023-02-05 10:21:52

Does this problem has anything to do with Mobius Inversion ?

rouge_kitty: 2022-08-29 18:41:11

you can check out my method here if you are getting a TLE and cannot figure out why: <snip>
[Simes]: No thanks, we don't want links to solutions.

Last edit: 2022-08-29 19:53:39
tadros: 2022-06-06 23:53:28

how could you solve this problem guys?

minhnguyent546: 2022-03-27 11:55:04

Just avoid t * sqrt(n)
I'm using generate all factor from prime factor and i get AC. Hope you guys get it

lakshya_1412: 2021-10-21 13:01:05

WA in ALL GO's

Vladimir Kirichenkoff: 2021-07-30 02:22:35

To solve this task perform next steps:
1. Fast factor base generation.
2. Find recurrent formula.

sankalp_7: 2021-06-27 17:13:18

If you are doing this question in O(n log n +t*sqrt(n) ) (TLE will come)
Means you know the concept.
Just to avoid sqrt(n) pre-compute answer just like sieve concept.

anikett: 2021-03-22 11:41:51

Don't solve in python :/ , AC in C++

mahbubsabuj: 2021-03-20 17:33:45

do not comment useless comment like ac in one go.

anisf: 2020-10-09 12:14:07

Accept in One GO!!!!!!!


Added by:Varun Jalan
Date:2010-01-24
Time limit:1s
Source limit:50000B
Memory limit:1536MB
Cluster: Cube (Intel G860)
Languages:All except: PERL6
Resource:own problem used for Codechef Snackdown Onsite