AFS  Amazing Factor Sequence
Bhelu is the classmate of Bablu who made the Amazing Prime Sequence .
He felt jealous of his classmate and decides to make his own sequence. Since he was not very imaginative, he came up with almost the same definition just making a difference in f(n):
 a[0] = a[1] = 0.
 For n > 1, a[n] = a[n  1] + f(n), where f(n) is the sum of positive integers in the following set S.
 S = {x  x < n and n % x = 0}.
Now, Bablu asked him to make a code to find f(n) as he already had the code of his sequence. So, Bhelu asks for your help since he doesn't know Programming. Your task is very simple, just find a[n] for a given value of n (< 10^6).
Input
Your code will be checked for multiple Test Cases.
First Line of Input contains T (<= 100), the number of Test Cases.
Next T lines contain a single positive integer N. (1 < N < 10^6).
Output
Single line containing a[n] i.e. nth number of the sequence for each test case.
Example
Input: 3 3 4 5 Output: 2 5 6
Explanation
f(2) = 1 {1} f(3) = 1 {1} f(4) = 3 {1, 2} f(5) = 1 {1}
hide comments
fighter_4:
20200413 14:32:55
Precomputation is just Amazing :D 

salman3007:
20181006 14:57:19
little modification in sieve algorithm 

zephyr_96:
20180518 23:02:25
Little modification to sieve will work :) Last edit: 20180518 23:12:51 

amulyagaur:
20170724 10:37:34
finally 100th.. :) 

bks19:
20170705 18:44:24
try to solve in O(n) otherwise TLE, precalculation is required 

pratyush2013:
20160720 19:35:44
this problem is easy if u r not overconfident...please focus more on problem statement Last edit: 20160720 19:36:13 

darkchocolate:
20160614 19:24:06
@Ankit got accepted after declaring array globally. Thanks! 

godfrey_17897:
20160210 18:00:06
modify sieve and you are done !!!! 

GAURAV CHANDEL:
20160131 14:25:49
I love precalculations.... 

shantanu tripathi:
20150917 19:28:33
o(n) also got accpted...hehe 
Added by:  c[R]@zY f[R]0G 
Date:  20130315 
Time limit:  1s 
Source limit:  5000B 
Memory limit:  1536MB 
Cluster:  Cube (Intel G860) 
Languages:  All except: ASM64 