Prime Power

A prime power is a prime or integer power of a prime. A test for a number  being a prime power will be implemented in the Wolfram Language as PrimePowerQ[n].

The first few prime powers are 2, 3, 4, 5, 7, 8, 9, 11, 13, 16, 17, 19, 23, 25, ... (OEIS A000961). The first few prime powers with power  are given by 4, 8, 9, 16, 25, 27, 32, 49, 64, 81, ... (OEIS A025475). The number of prime powers (exponents ) up to  is given by

(Hardy 1999, p. 27).

The following table gives prime th powers.

	OEIS	prime th powers
1	A000040	2, 3, 5, 7, 11, 13, 17, 19, 23, ...
2	A001248	4, 9, 25, 49, 121, 169, 289, 361, ...
3	A030078	8, 27, 125, 343, 1331, 2197, 4913, ...
4	A030514	16, 81, 625, 2401, 14641, 28561, 83521, ...
5	A050997	32, 243, 3125, 16807, 161051, 371293, ...

REFERENCES:

Hardy, G. H. Ramanujan: Twelve Lectures on Subjects Suggested by His Life and Work, 3rd ed. New York: Chelsea, 1999.

Sloane, N. J. A. Sequences A000040/M0652, A000961/M0517, A001248, A025475, A030078, A030514, and A050997 in "The On-Line Encyclopedia of Integer Sequences."