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Oct 30, 2017 at 19:39 comment added shreevatsa It's been mentioned in comments on another answer, but just for completeness: these numbers are known as superior highly composite numbers following Ramanujan, and they (A002201) form a subsequence of the highly composite numbers (A002182) which in turn are all possible values of $f(n)$ for the $f$ in the question.
Oct 28, 2017 at 12:34 vote accept Joseph O'Rourke
Nov 4, 2017 at 16:48
Oct 28, 2017 at 6:29 history answered Will Sawin CC BY-SA 3.0