Maximally divisible number

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Maximally divisible numbers (sequence A007416 in OEIS) are integers n which have more divisors than any other integer m smaller than n.

For example, 12 is the smallest integer with six divisors (1, 2, 3, 4, 6, and 12), therefore it is a maximally divisible number. Here is a list of smallest ones: 1, 2, 4, 6, 12, 16, 24, 36, 48, 60, 64, 120, 144, 180, 192, 240, 360, 576, 720, 840, 900, 960, 1024, 1260, 1296, 1680, 2520, 2880, 3072, 3600, 4096, 5040, 5184, 6300, 6480, 6720, 7560, 9216, 10080 ...

This concept was first defined by Srinivasa Ramanujan and later independently by the Automated Mathematician.