## Project Euler Problem #23

### February 9, 2010

Read the details of the problem here

Summary

Find the sum of all the positive integers which cannot be written as the sum of two abundant numbers.

Solution

FAIL. Sad to say but this one defeated me – I just couldn’t get it to break the 15 second limit when using Groovy. My initial implementation used various Groovy features like adding `isAbundant()` and `sumOfProperDivisors()` methods to the Integer class and accumulating abundant numbers in lists, etc. but the runtime was 55 seconds. Gradually removing these syntactical niceties and using more inline code got me back to 21.2 seconds. I could have opted again for a multi-threaded approach similar to that which I took for Solution #14 and that would have probably got me down to below 15 seconds but I took the easy way out and ported it over to Java.

```import java.util.Arrays;

final int LO_VAL = 12;
final int HI_VAL = 28123+1;

boolean[] isAbundant = new boolean[HI_VAL-LO_VAL+1];
Arrays.fill(isAbundant, false);

for (int i = LO_VAL; i <= HI_VAL-LO_VAL; i++) {
int sum = 1;
int sqrt = (int)Math.sqrt(i);
for (int d = 2; d <= sqrt; d++) {
if (i % d == 0) sum += d + i / d;
}
if (sqrt * sqrt == i) sum -= sqrt;
isAbundant[i] = (sum > i);
}

boolean[] nums = new boolean[HI_VAL];
Arrays.fill(nums, false);

for (int i = LO_VAL; i < isAbundant.length; i++) {
if (isAbundant[i]) {
for (int j = i; j  < isAbundant.length; j++) {
if (isAbundant[j]) {
int sum = i + j;
if (sum >= HI_VAL) break;
nums[sum] = true;
}
}
}
}