Prime Power
المؤلف:
Hardy, G. H
المصدر:
Ramanujan: Twelve Lectures on Subjects Suggested by His Life and Work, 3rd ed. New York: Chelsea, 1999.
الجزء والصفحة:
...
7-10-2020
1314
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."
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