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%I #16 Dec 21 2020 02:23:11
%S 4,8,9,25,27,49,121,125,169,289,343,361,529,841,961,1331,1369,1681,
%T 1849,2197,2209,2809,3481,3721,4489,4913,5041,5329,6241,6859,6889,
%U 7921,9409,10201,10609,11449,11881,12167,12769,16129,17161,18769,19321,22201
%N Squares and cubes of primes.
%C Primitive elements for powerful numbers; every powerful is product of these numbers. The representation is not necessarily unique.
%C A178254(a(n)) = 2. - _Reinhard Zumkeller_, May 24 2010
%F Sum_{n>=1} 1/a(n) = P(2) + P(3) = 0.6270100593..., where P is the prime zeta function. - _Amiram Eldar_, Dec 21 2020
%t m=30000;Union[Prime[Range[PrimePi[m^(1/2)]]]^2,Prime[Range[PrimePi[m^(1/3)]]]^3] (* _Vladimir Joseph Stephan Orlovsky_, Apr 11 2011 *)
%t With[{nn=50},Take[Union[Flatten[Table[{n^2,n^3},{n,Prime[Range[ nn]]}]]],nn]] (* _Harvey P. Dale_, Feb 26 2015 *)
%o (PARI) for(n=1,40000,fm=factor(n);if(matsize(fm)[1]==1&(fm[1,2]==2|fm[1,2]==3),print1(n",")))
%o (PARI) is(n)=my(k=isprimepower(n)); k && k<4 \\ _Charles R Greathouse IV_, May 24 2013
%Y Cf. A001694, A053810, A001248, A030078, A087797.
%K nonn
%O 1,1
%A _Franklin T. Adams-Watters_, Nov 23 2009
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