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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

This might be interesting:

Moreover if you care about sums:

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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

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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