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%I #15 May 22 2020 16:21:34
%S 32,243,3125,7776,16807,100000,161051,371293,537824,759375,1419857,
%T 2476099,4084101,5153632,6436343,11881376,20511149,24300000,28629151,
%U 39135393,45435424,52521875,69343957,79235168,90224199,115856201
%N Numbers whose prime factors are raised to the fifth power.
%F Sum_{k>=1} 1/a(k) = zeta(5)/zeta(10) - 1 = A157291 - 1. - _Amiram Eldar_, May 22 2020
%e 7776 = 32*243 = 2^5*3^5 so the prime factors, 2 and 3, are raised to the fifth power.
%t Select[ Range@41^5, Union[Last /@ FactorInteger@# ] == {5} &] (* _Robert G. Wilson v_ *)
%t Rest[Select[Range[100], SquareFreeQ]^5] (* _Vaclav Kotesovec_, May 22 2020 *)
%o (PARI) allpwrfact(n,p) = \All prime factors are raised to the power p { local(x,j,ln,y,flag); for(x=4,n, y=Vec(factor(x)); ln = length(y[1]); flag=0; for(j=1,ln, if(y[2][j]==p,flag++); ); if(flag==ln,print1(x",")); ) }
%Y Proper subset of A000584.
%Y Nonunit terms of A329332 column 5 in ascending order.
%Y Cf. A157291.
%K easy,nonn
%O 4,1
%A _Cino Hilliard_, Jan 25 2006
%E More terms from _Robert G. Wilson v_, Jan 26 2006
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