Alice and Pairs
Tag(s):

## Easy-Medium, Math, Number Theory, Prime Factorization, Sieve

Problem
Editorial
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Alice is very good in mathematics. So, his teacher gave him a number N and wants from him to count total number of pairs, such that $gcd( x ,y )=1$ and $x*y=N$, where $(x, y)$ forms a pair.

Alice is very busy in his exams and he wants your help .So solve this problem for Alice.

Input:
Input starts with a number T and then follows T lines contains a single number, N.

Output:
Find the total number of pairs, and print the required answer in a new line.

Constraints:
$1 \le T \le 10^5$
$1 \le N \le 10^7$

SAMPLE INPUT
2
2
6

SAMPLE OUTPUT
2
4

Explanation

For 1st test case, pairs are (1,2) and (2,1)

For 2nd test case, pairs are (1,6) , (6,1) , (2,3) and (3,2).

Time Limit: 1.0 sec(s) for each input file.
Memory Limit: 256 MB
Source Limit: 1024 KB
Marking Scheme: Marks are awarded when all the testcases pass.
Allowed Languages: C, C++, C++14, Clojure, C#, D, Erlang, F#, Go, Groovy, Haskell, Java, Java 8, JavaScript(Rhino), JavaScript(Node.js), Julia, Kotlin, Lisp, Lisp (SBCL), Lua, Objective-C, OCaml, Octave, Pascal, Perl, PHP, Python, Python 3, R(RScript), Racket, Ruby, Rust, Scala, Swift, Swift-4.1, Visual Basic

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## This Problem was Asked in

Challenge Name

Sapient Global Markets Core Java Hiring Challenge

OTHER PROBLEMS OF THIS CHALLENGE
• Math > Basic Math
• Math > Number Theory