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.
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 number
In mathematics, the natural numbers are those numbers used for counting (as in "there are ''six'' coins on the table") and ordering (as in "this is the ''third'' largest city in the country").
Numbers used for counting are called '' cardinal ...
s 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
In number theory, the aliquot sum ''s''(''n'') of a positive integer ''n'' is the sum of all proper divisors of ''n'', that is, all divisors of ''n'' other than ''n'' itself.
That is,
:s(n)=\sum\nolimits_d.
It can be used to characterize the prime ...
.
References
{{Classes of natural numbers
Divisor function
Integer sequences
Number theory