Sequence: smallest number with exactly n divisors

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Sequence: smallest number with exactly n divisors is a draft programming task. It is not yet considered ready to be promoted as a complete task, for reasons that should be found in its talk page.

Calculate the sequence where each term an is the smallest natural numbers that has exactly n divisors.

See: OEIS:A005179

Task

Show here, on this page, at least the first 15 terms of the sequence.