Prove that among any 12 consecutive positive integers there is at least one which is smaller than the sum of its proper divisors. (The proper divisors of a positive integer n are all positive integers other than 1 and n which divide n. For example, the proper divisors of 14 are 2 and 7)
2026-04-08 12:34:57.1775651697
Prove that among any 12 consecutive positive integers there is at least one which is smaller than the sum of its proper divisors
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Hint: Among any $12$ consecutive positive integers, there is one that is a multiple of $12$.
Can you show that $12n$ is smaller than the sum of its divisors for any positive integer $n$?