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

REFERENCES:

Sloane, N. J. A. Sequences A118914 in "The On-Line Encyclopedia of Integer Sequences."