amicable examples with proof.
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Example of Amicable Pair
220 and 284 are the smallest amicable pair:
σ(220)=σ(284)=504=220+284
Proof
Let s(n) denote the aliquot sum of n.
By definition:
s(n)=σ(n)−n
where σ(n) denotes the σ function.
Thus:
s(220) = σ(220)−220
= 504−220 σ of 220
= 284
s(284) = σ(284)−284
= 504−284 σ of 284
= 220
It can be determined by inspection of the aliquot sums of all smaller integers that there is no smaller amicable pair.
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what is the meaning of amicable
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