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An amenable number is a positive integer for which there exists a multiset of as many integers as the original number that both add up to the original number and when multiplied together give the original number. To put it algebraically, for a positive integer n, there is a multiset of n integers {a1, ..., an}, for which the equalities
hold. Negative numbers are allowed in the multiset. For example, 5 is amenable since 5 = 1 + (−1) + 1 + (−1) + 5. All and only those numbers congruent to 0 or 1, except 4, are amenable.
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