Can you show me C plus plus function that displays perfect number?

Answer 1

A perfect number is a positive integer that is equal to the sum of its positive divisors other than itself. Thus 6 is a perfect number because it has divisors 1, 2 and 3, the sum of which is 6.

There are actually very few perfect numbers in any given range, so rather than waste precious CPU cycles determining the divisors of a number and then summing them to see if it is perfect or not (most of the time it won't be) it is much easier and quicker to simply store them in a static array.

A 64-bit unsigned integer can store values in the range 0 to 18,446,744,073,709,551,615, but there are only 8 perfect numbers in this range. Thus the following array will suffice:

unsigned long long perfect = {6, 28, 496, 8128, 33550336, 8589869056, 137438691328, 2305843008139952128 };

To determine if a given positive value is perfect or not, simply test to see if it exists in this array. The following function shows how this can be achieved.

bool is_perfect(const unsigned long long value)

{

const unsigned long long perfect[8] = {6, 28, 496, 8128, 33550336, 8589869056, 137438691328, 2305843008139952128};

for(unsigned i=0; i<8; ++i)

if(value==perfect[i])

return true;

return false;

}