Prime Power

A prime power is a prime or positive integer power of a prime. A test for a number being a prime is 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, ...