18 lines
770 B
Markdown
18 lines
770 B
Markdown
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The proper divisors of a number are all the divisors excluding the number itself.
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For example, the proper divisors of 28 are 1, 2, 4, 7, and 14.
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As the sum of these divisors is equal to 28, we call it a perfect number.
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Interestingly the sum of the proper divisors of 220 is 284 and the sum of the
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proper divisors of 284 is 220, forming a chain of two numbers.
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For this reason, 220 and 284 are called an amicable pair.
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Perhaps less well known are longer chains.
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For example, starting with 12496, we form a chain of five numbers:
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~~~
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12496 -> r -> 15472 -> 14536 -> 14264 (-> 12496 -> ...)
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~~~
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Since this chain returns to its starting point, it is called an amicable chain.
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Find the smallest member of the longest amicable chain with no element exceeding one million.
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