Prime Signature
The prime signature of a positive integer 
is a sorted list
of nonzero exponents 
in the prime
factorization
 |
By definition, the prime signature of 1 is 
. The prime numbers
have prime signature 
and squares of prime numbers have
prime signature 
.
The following table gives the prime signatures of the first few positive integers (OEIS A118914).
 | factorization | prime signature |  | factorization | prime signature |
| 1 | 1 |  | 11 | 11 |  |
| 2 | 2 |  | 12 |  |  |
| 3 | 3 |  | 13 | 13 |  |
| 4 |  |  | 14 |  |  |
| 5 | 5 |  | 15 |  |  |
| 6 |  |  | 16 |  |  |
| 7 | 7 |  | 17 | 17 |  |
| 8 |  |  | 18 |  |  |
| 9 |  |  | 19 | 19 |  |
| 10 |  |  | 20 |  |  |
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prime factorization