%I #19 Oct 13 2020 05:45:08

%S 64,729,15625,46656,117649,1000000,1771561,4826809,7529536,11390625,

%T 24137569,47045881,85766121,113379904,148035889,308915776,594823321,

%U 729000000,887503681,1291467969,1544804416,1838265625,2565726409,3010936384,3518743761,4750104241

%N Numbers whose prime factors are raised to the sixth power.

%H Nathaniel Johnston, <a href="/A113851/b113851.txt">Table of n, a(n) for n = 1..5000</a>

%F a(n) = A005117(n+1)^6. - _Nathaniel Johnston_, Jun 21 2011

%F Sum_{n>=1} 1/a(n) = zeta(6)/zeta(12) - 1 = A269404 - 1. - _Amiram Eldar_, Oct 13 2020

%p for n from 2 to 100 do if(numtheory[issqrfree](n))then printf("%d, ", n^6): fi: od: # _Nathaniel Johnston_, Jun 21 2011

%t Select[ Range@37^6, Union[Last /@ FactorInteger@# ] == {6} &] (* _Robert G. Wilson v_ *)

%t Select[Range[2, 37], SquareFreeQ]^6 (* _Amiram Eldar_, Oct 13 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 Subset of A001014. Superset of A030516.

%Y Nonunit terms of A329332 column 6 in ascending order.

%Y Cf. A005117, A269404.

%K easy,nonn

%O 1,1

%A _Cino Hilliard_, Jan 25 2006

%E More terms from _Robert G. Wilson v_, Jan 26 2006