A prime power is a prime or integer power of a prime . A test for a number 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 A025475 ).
The number of prime powers (exponents
(Hardy 1999, p. 27).
The following table gives prime
OEIS prime 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, ...
See also Prime Number ,
Solitary
Number
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References Hardy, G. H. Ramanujan: Twelve Lectures on Subjects Suggested by His Life and Work, 3rd ed. Sloane, N. J. A. Sequences A000040 /M0652,
A000961 /M0517, A001248 ,
A025475 , A030078 ,
A030514 , and A050997
in "The On-Line Encyclopedia of Integer Sequences." Referenced
on Wolfram|Alpha Prime Power
Cite this as:
Weisstein, Eric W. "Prime Power." From
MathWorld https://mathworld.wolfram.com/PrimePower.html
Subject classifications
being a prime is implemented in the Wolfram
Language as PrimePowerQ[n].
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
th powers.
th powers