

A168363


Squares and cubes of primes.


9



4, 8, 9, 25, 27, 49, 121, 125, 169, 289, 343, 361, 529, 841, 961, 1331, 1369, 1681, 1849, 2197, 2209, 2809, 3481, 3721, 4489, 4913, 5041, 5329, 6241, 6859, 6889, 7921, 9409, 10201, 10609, 11449, 11881, 12167, 12769, 16129, 17161, 18769, 19321, 22201
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OFFSET

1,1


COMMENTS

Primitive elements for powerful numbers; every powerful is product of these numbers. The representation is not necessarily unique.
A178254(a(n)) = 2.  Reinhard Zumkeller, May 24 2010


LINKS

Table of n, a(n) for n=1..44.


MATHEMATICA

m=30000; Union[Prime[Range[PrimePi[m^(1/2)]]]^2, Prime[Range[PrimePi[m^(1/3)]]]^3] (* Vladimir Joseph Stephan Orlovsky, Apr 11 2011 *)
With[{nn=50}, Take[Union[Flatten[Table[{n^2, n^3}, {n, Prime[Range[ nn]]}]]], nn]] (* Harvey P. Dale, Feb 26 2015 *)


PROG

(PARI) for(n=1, 40000, fm=factor(n); if(matsize(fm)[1]==1&(fm[1, 2]==2fm[1, 2]==3), print1(n", ")))
(PARI) is(n)=my(k=isprimepower(n)); k && k<4 \\ Charles R Greathouse IV, May 24 2013


CROSSREFS

Cf. A001694, A053810, A001248, A030078, A087797.
Sequence in context: A076702 A051761 A153326 * A182046 A171468 A114377
Adjacent sequences: A168360 A168361 A168362 * A168364 A168365 A168366


KEYWORD

nonn


AUTHOR

Franklin T. AdamsWatters, Nov 23 2009


STATUS

approved



