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Doubly Perfect

Posted: February 5, 2024

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Let sigma(n) be the sum of all positive divisors of n. For example sigma(6) = 1 + 2 + 3 + 6 = 12 since the positive divisors of 6 are (1,2,3,6). Notice that sigma(6) = 2(6), therefore 6 is called a perfect number. We can call n doubly perfect if sigma(sigma(n)) = 4(n). For example, 15 is doubly perfect because sigma(15) = 24 and sigma(24) = 60 which is 4(15). Find the next doubly perfect integer greater than 15.

Problem submitted by Pat Costello, Eastern Kentucky University

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