A prime power is a positive integer of the form prime and positive integer .
A test for an integer 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 A246655 ). The first few prime powers
with power A246547 ).
Let exponents
at least 2 and value at most
where prime
counting function and floor function (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 Odd Prime Power ,
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,
A246655 , A001248 ,
A246547 , 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
, where 
is a prime and 
is a positive integer.
A test for an integer 
being a prime power is implemented in the Wolfram
Language as PrimePowerQ[n].
are given by 4, 8, 9, 16, 25, 27, 32, 49, 64, 81, ... (OEIS A246547).
Let 
count the prime powers with exponents
at least 2 and value at most 
, where 
. Then
is the prime
counting function and 
is the floor function (Hardy 1999, p. 27).
th powers.
th powers