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]
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
- ^ 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.
- ^ Dickson, L. E. (1913). "Amicable Number Triples". The American Mathematical Monthly. 20 (3): 84–92. doi:10.2307/2973442. ISSN 0002-9890. JSTOR 2973442.
- ^ 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.
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Divisibility-based sets of integers
- Integer factorization
- Divisor
- Unitary divisor
- Divisor function
- Prime factor
- Fundamental theorem of arithmetic
- Untouchable
- Amicable (Triple)
- Sociable
- Betrothed
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