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euler023.c
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euler023.c
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/* https://projecteuler.net/problem=23
* A perfect number is a number for which the sum of its proper divisors is
* exactly equal to the number. For example, the sum of the proper divisors of
* 28 would be 1 + 2 + 4 + 7 + 14 = 28, which means that 28 is a perfect number.
*
* A number n is called deficient if the sum of its proper divisors is less than
* n and it is called abundant if this sum exceeds n.
*
* As 12 is the smallest abundant number, 1 + 2 + 3 + 4 + 6 = 16, the smallest
* number that can be written as the sum of two abundant numbers is 24. By
* mathematical analysis, it can be shown that all integers greater than 28123
* can be written as the sum of two abundant numbers. However, this upper limit
* cannot be reduced any further by analysis even though it is known that the
* greatest number that cannot be expressed as the sum of two abundant numbers
* is less than this limit.
*
* Find the sum of all the positive integers which cannot be written as the sum
* of two abundant numbers.
*
* David Timm 2014-09-21
*/
#include <stdio.h>
int factor_add(int);
int main(void)
{
int i, j;
int total = 0;
int count = 0;
int current;
int abundant[24124];
int matches[24124];
matches[0] = 0;
for(i=1;i<24124;i++)
{
if(i < factor_add(i))
{
abundant[count] = i;
count++;
}
matches[i] = 1;
}
for(i=0;i<count;i++)
{
for(j=i;j<count;j++)
{
current = abundant[i] + abundant[j];
if(current < 24124) matches[current] = 0;
}
}
for(i=1;i<24124;i++)
{
total += matches[i] * i;
}
printf("%d\n", total);
}
int factor_add(int number)
{
int i;
int total = 1;
for(i=2; i<(number/2 + 1); i++)
{
if(number%i == 0) total += i;
}
return total;
}