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Numbers whose prime factors are raised to the seventh power.
6

%I #14 Oct 13 2020 05:45:16

%S 128,2187,78125,279936,823543,10000000,19487171,62748517,105413504,

%T 170859375,410338673,893871739,1801088541,2494357888,3404825447,

%U 8031810176,17249876309,21870000000,27512614111,42618442977,52523350144,64339296875,94931877133,114415582592

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

%H Amiram Eldar, <a href="/A113852/b113852.txt">Table of n, a(n) for n = 1..10000</a>

%F From _Amiram Eldar_, Oct 13 2020: (Start)

%F a(n) = A005117(n+1)^7.

%F Sum_{n>=1} 1/a(n) = zeta(7)/zeta(14) - 1. (End)

%t Select[ Range@34^7, Union[Last /@ FactorInteger@# ] == {7} &] (* _Robert G. Wilson v_ *)

%t Select[Range[2, 34], SquareFreeQ]^7 (* _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 Proper subset of A001015.

%Y Nonunit terms of A329332 column 7 in ascending order.

%Y Cf. A005117, A013665, A013672.

%K easy,nonn

%O 1,1

%A _Cino Hilliard_, Jan 25 2006

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