Perfect numbers: Difference between revisions

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Remove unnecessary iteration and logically redundant test (if [sum == 2 * num] then [sum - num == num] for all positive num anyway).
m Added wp ref and fixed definition - see discussion
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{{task|Discrete math}}Write a function which says whether a number is perfect.
{{task|Discrete math}}Write a function which says whether a number is perfect.


A number is perfect if the sum of its factors is equal to twice the number. An equivalent condition is that <tt>n</tt> is perfect if the sum of <tt>n</tt>'s factors that are less than <tt>n</tt> is equal to <tt>n</tt>.
[[wp:Perfect_numbers|A perfect number]] is a positive integer that is the sum of its proper positive divisors excluding the number itself. Equivalently, a perfect number is a number that is half the sum of all of its positive divisors (including itself).


Note: The faster [[Lucas-Lehmer test]] is used to find primes of the form 2<sup>''n''</sup>-1, all ''known'' perfect numbers can be derived from these primes using the formula (2<sup>''n''</sup> - 1) × 2<sup>''n'' - 1</sup>. It is not known if there are any odd perfect numbers.
Note: The faster [[Lucas-Lehmer test]] is used to find primes of the form 2<sup>''n''</sup>-1, all ''known'' perfect numbers can be derived from these primes using the formula (2<sup>''n''</sup> - 1) × 2<sup>''n'' - 1</sup>. It is not known if there are any odd perfect numbers.
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