GCDEX - GCD Extreme


Given the value of N, you will have to find the value of G. The meaning of G is given in the following code

G = 0;
for (i = 1; i < N; i++)
  for (j = i+1; j <= N; j++) 
    G += gcd(i, j);
Here gcd() is a function that finds the greatest common divisor of the two input numbers.

Input

The input file contains at most 20000 lines of inputs. Each line contains an integer N (1 < N < 1000001). The meaning of N is given in the problem statement. Input is terminated by a line containing a single zero.

Output

For each line of input produce one line of output. This line contains the value of G for the corresponding N. The value of G will fit in a 64-bit signed integer.

Example

Input:
10
100
200000
0

Output:
67
13015
143295493160

Time limit has been changed. Some AC solutions get TLE

hide comments
badboy_1496: 2018-07-17 06:08:56

hurray!!!! ac in one go...nice way of using sieves

excel_blaze: 2018-05-21 16:07:54

simple logic and implementation(^_^)
nice for beginners

Last edit: 2018-05-21 16:08:46
nadstratosfer: 2018-03-21 19:09:52

Took me 7+ hours in 3 sittings to fit within this retarded TL in PyPy. Props to julkas for showing it's possible.

anupamwadhwa: 2018-02-07 19:30:21

Try NTG after this one.

include_sajal: 2018-01-13 18:13:41

Using Euler Phi will bring extra overheads. Try something different. Though one can apply Euler Phi cautiously to get AC. BTW, an awesome one!

chetan4060: 2018-01-01 11:00:39

very good concept mobius function.

Last edit: 2018-04-16 21:05:26
vib_s02: 2017-09-02 15:12:56

How does one find all divisors of N multiple times?

hacker_sk: 2016-09-25 15:54:50

AC in one go :D.. 0.27 sec
Really nice problem.. it will clear all the concepts related to gcd and totient.

Last edit: 2016-09-30 20:01:11
mkfeuhrer: 2016-08-15 11:23:29

euler phi :-)

visvats_141095: 2016-06-17 15:05:26

9 tle and finally accepted! learnt a lot from this question!


Added by:Phenomenal
Date:2009-02-16
Time limit:0.237s
Source limit:50000B
Memory limit:1536MB
Cluster: Cube (Intel G860)
Languages:All except: ERL JS-RHINO NODEJS PERL6 VB.NET
Resource:ACM World Final Warm up 1 - 2008