The difficulty level gets ramped up here in Project Euler’s next problem.

## Problem 21:

### Amicable Numbers

Let d(n) be defined as the sum of proper divisors of n (numbers less than n which divide evenly into n).

If d(a) = b and d(b) = a, where a ≠ b, then a and b are an amicable pair and each of a and b are called amicable numbers.For example, the proper divisors of 220 are 1, 2, 4, 5, 10, 11, 20, 22, 44, 55 and 110; therefore d(220) = 284. The proper divisors of 284 are 1, 2, 4, 71 and 142; so d(284) = 220.

Evaluate the sum of all the amicable numbers under 10000.

Check this post to see the types and functions used in this solution.

DECLARE divisors_array euler_pkg.int_array := euler_pkg.int_array(); sumz INTEGER := 0; upper_limit INTEGER := 10000; BEGIN FOR i IN 1..upper_limit LOOP sumz := 0; divisors_array := euler_pkg.get_divisors(i); for e in 1 .. divisors_array.count loop IF divisors_array(e) != i THEN sumz := divisors_array(e) + sumz; END IF; end loop; INSERT INTO amicable_numbers VALUES (i, sumz); COMMIT; END LOOP; END; SELECT sum(sum_divisors) FROM amicable_numbers a WHERE EXISTS (SELECT 1 FROM amicable_numbers WHERE sum_divisors = a.number_in AND a.sum_divisors = number_in) AND number_in != sum_divisors; --output 31626

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