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2003 BAMO p1 perfect number is factorial also

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August 26, 2019
factorialperfect numbernumber theorydivisor

Problem Statement

An integer is a perfect number if and only if it is equal to the sum of all of its divisors except itself. For example, 2828 is a perfect number since 28=1+2+4+7+1428 = 1 + 2 + 4 + 7 + 14. Let n!n! denote the product 1⋅2⋅3⋅...⋅n1\cdot 2\cdot 3\cdot ...\cdot n, where nn is a positive integer. An integer is a factorial if and only if it is equal to n!n! for some positive integer nn. For example, 2424 is a factorial number since 24=4!=1⋅2⋅3⋅424 = 4! = 1\cdot 2\cdot 3\cdot 4. Find all perfect numbers greater than 11 that are also factorials.
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