All Tracks Math Number Theory Basic Number Theory-2 Problem

Count of integers
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Algorithms, Euler's totient function, Greatest common divisor, Math, Number Theory, Sieve

Problem
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You are given a positive integer \(n\), for \(Q\) queries, You are required to determine the number of integers \(k\) (\(1 \leq k \leq n\)) such that \(gcd(k,n)\hspace{2mm}!= 1\) and \(gcd(k,n)\hspace{2mm}!= k\).

Input format

  • First line: Integer \(Q\) denoting the number of queries
  • Next \(Q\) lines: Integer \(n\)

Output format

Print \(Q\) lines each containing an integer that denotes the answer to that specific query.

Constraints

\(1 \leq Q \leq 10^5\)

\(1 \leq n \leq 10^6\)

SAMPLE INPUT
1
10
SAMPLE OUTPUT
3
Explanation

For c = {1,3,7,9} gcd(c,10) = 1

For c = {2,5,10} gcd(c,10) = c

gcd(4,10) = 2

gcd(6,10) = 2

gcd(8,10) = 2

So, answer is 3.

Time Limit: 1.0 sec(s) for each input file.
Memory Limit: 256 MB
Source Limit: 1024 KB

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