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I vaguely remember there is a notion of numbers rich in divisors, i.e. (number of divisors of N)/N is comparatively large. What's their name? Given a number M, how could I find such a number in its neighbourhood?

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Primorials $p_n \#$ have quite some divisors. –  draks ... Sep 24 '12 at 10:52
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2 Answers 2

This might be interesting: http://en.wikipedia.org/wiki/Highly_composite_number

Moreover if you care about sums: http://en.wikipedia.org/wiki/Abundant_number

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wow I never knew pure mathematicians even studied these things. The names themselves are funny enough. –  Xiaowen Li Sep 24 '12 at 11:48
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You might be thinking about smooth numbers.

How to find such things? I suppose you could just multiply small numbers together until you are within the "neighbourhood". If you overshoot, take out some factors and replace them with other factors.

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