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Demonstration, with
Cuisenaire rods, that the number 10 is an unusual number, its largest prime factor being 5, which is greater than √10 ≈ 3.16
In number theory, an unusual number is a natural number n whose largest prime factor is strictly greater than ${\sqrt {n))$.
A ksmooth number has all its prime factors less than or equal to k, therefore, an unusual number is non${\sqrt {n))$smooth.
Relation to prime numbers
All prime numbers are unusual.
For any prime p, its multiples less than p² are unusual, that is p, ... (p1)p, which have a density 1/p in the interval (p,p²).
Examples
The first few unusual numbers are
 2, 3, 5, 6, 7, 10, 11, 13, 14, 15, 17, 19, 20, 21, 22, 23, 26, 28, 29, 31, 33, 34, 35, 37, 38, 39, 41, 42, 43, 44, 46, 47, 51, 52, 53, 55, 57, 58, 59, 61, 62, 65, 66, 67.... (sequence A064052 in the OEIS)
The first few nonprime unusual numbers are
 6, 10, 14, 15, 20, 21, 22, 26, 28, 33, 34, 35, 38, 39, 42, 44, 46, 51, 52, 55, 57, 58, 62, 65, 66, 68, 69, 74, 76, 77, 78, 82, 85, 86, 87, 88, 91, 92, 93, 94, 95, 99, 102....
Distribution
If we denote the number of unusual numbers less than or equal to n by u(n) then u(n) behaves as follows:
n

u(n)

u(n) / n

10

6

0.6

100

67

0.67

1000

715

0.72

10000

7319

0.73

100000

73322

0.73

1000000

731660

0.73

10000000

7280266

0.73

100000000

72467077

0.72

1000000000

721578596

0.72

Richard Schroeppel stated in 1972 that the asymptotic probability that a randomly chosen number is unusual is ln(2). In other words:
 $\lim _{n\rightarrow \infty }{\frac {u(n)}{n))=\ln(2)=0.693147\dots \,.$