A prime power is a prime or integer power of a prime. A test for a number n 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 >=2 are given by 4, 8, 9, 16, 25, 27, 32, 49, 64, 81, ... (OEIS A025475). The number of prime powers (exponents >=2) up to x is given by x^(1/2) + x^(1/3) + x^(1/4) + ... = O(x^(1/2) ln x) (Hardy 1999, p. 27). The following table gives prime kth powers.

prime number | solitary number