Amicable Numbers Checker

How it is calculated

The tool finds the aliquot sum s(n), the sum of all divisors of n except n itself. It does this by testing every i from 2 up to √n, adding both i and n ÷ i whenever i divides n, and starting from 1. The number s(n) is shown as the partner. It then computes s(partner). The pair is called amicable only when s(n) = partner, s(partner) = n and the partner differs from n. A perfect number such as 6 has itself as partner, so it is reported as not amicable. Whole numbers from 1 to 100,000,000 are accepted; a decimal is cut to its integer part and anything outside the range returns no result. For 1 the partner is 0. Note that the partner is shown even when the answer is no, since it is simply the aliquot sum.

Common mistakes

• Including the number itself in the divisor sum. Amicable numbers use proper divisors only, which is why 220 pairs with 284 and not with 504.
• Seeing a partner and assuming a pair. The partner is displayed for every number; only the status line says whether it leads back to the starting number.
• Expecting perfect numbers such as 6 or 28 to count. They map to themselves, so the tool reports them as not amicable.
• Looking for pairs by trial with small numbers. The smallest pair is 220 and 284, and pairs are rare, so most entries give “Not amicable”.
• Entering a number above 100,000,000, which returns no result, or entering a decimal and expecting it to be rounded; it is truncated.