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#include <iostream>
#include <algorithm>
#include <map>
#include <vector>
#include <numeric>
#include <iterator>
std::vector<int> primeDecompose( int n ) {
std::vector<int> primeFactors ;
int current = 2 ;
while ( n != 1 ) {
if ( n % current == 0 ) {
primeFactors.push_back( current ) ;
n /= current ;
}
else {
current++ ;
}
}
return primeFactors ;
}
int my_gcd( int a , int b ) {
std::vector<int> firstFactors( primeDecompose( a ) ) ;
std::vector<int> secondFactors( primeDecompose( b ) ) ;
std::vector<int> common ;
std::set_intersection( firstFactors.begin( ) , firstFactors.end( ) ,
secondFactors.begin( ) , secondFactors.end( ) ,
std::inserter( common, common.begin( ) )) ;
return std::accumulate( common.begin( ) , common.end( ) , 1 ,
std::multiplies( ) ) ;
}
bool isAchilles( int n ) {
std::vector<int> primeFactors( primeDecompose( n ) ) ;
std::map<int , int> factorCount ;
for ( int i : primeFactors ) {
factorCount[ i ]++ ;
}
std::vector<int> exponents ;
for ( auto it = factorCount.begin( ) ; it != factorCount.end( ) ; ++it ) {
exponents.push_back( it->second ) ;
}
if ( *std::min_element(exponents.begin( ) , exponents.end( ) ) >= 2 ) {
int start = *exponents.begin( ) ;
return (std::accumulate( exponents.begin( ) , exponents.end( ) , start ,
[]( int a , int b ){ return my_gcd( a , b ) ; } ) == 1 ) ;
}
else
return false ;
}
int main( ) {
std::vector<int> achillesNumbers ;
int current = 2 ;
while ( achillesNumbers.size( ) != 20 ) {
if ( isAchilles( current ) ) {
achillesNumbers.push_back( current ) ;
}
current++ ;
}
for ( int i : achillesNumbers )
std::cout << i << " " ;
std::cout << std::endl ;
return 0 ;
}
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