Unusual number

Unusual number

In number theory, an unusual number is a natural number "n" whose largest prime factor is strictly greater than sqrt{n} OEIS|id=A064052. All prime numbers are unusual.

Richard Schroeppel proved in 1972 that the probability that a randomly chosen number is unusual is ln(2). Importantly, this is independent of the magnitude of the number chosen, as shown in the following table:

The proportions can be seen to be converging on ln(2) = 0.693147....

A "k"-smooth number has all its prime factors less than or equal to "k", therefore, an unusual number is non-sqrt{n}-smooth.

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