Amicable triple

In mathematics, an amicable triple is a set of three different numbers so related that the restricted sum of the divisors of each is equal to the sum of other two numbers.^[1][2]

Main article: Amicable numbers § Amicable tuples

In another equivalent characterization, an amicable triple is a set of three different numbers so related that the sum of the divisors of each is equal to the sum of the three numbers.

So a triple (a, b, c) of natural numbers is called amicable if s(a) = b + c, s(b) = a + c and s(c) = a + b, or equivalently if σ(a) = σ(b) = σ(c) = a + b + c. Here σ(n) is the sum of all positive divisors, and s(n) = σ(n) − n is the aliquot sum.^[3]

References

1. Dickson, L. E. (1913-03-01). "Amicable Number Triples". The American Mathematical Monthly. 20 (3): 84–92. doi:10.1080/00029890.1913.11997926. ISSN 0002-9890.
2. Dickson, L. E. (1913). "Amicable Number Triples". The American Mathematical Monthly. 20 (3): 84–92. doi:10.2307/2973442. ISSN 0002-9890. JSTOR 2973442.
3. Mason, Thomas E. (1921). "On Amicable Numbers and Their Generalizations". The American Mathematical Monthly. 28 (5): 195–200. doi:10.2307/2973750. ISSN 0002-9890. JSTOR 2973750.