A316499 - OEIS

%I #9 Jul 06 2018 17:11:18

%S 2048,9216,13824,20736,25600,31104,46656,50176,64000,69984,104976,

%T 115200,123904,157464,160000,172800,173056,175616,177147,225792,

%U 236196,259200,288000,338688,388800,400000,432000,508032,557568,583200,614656,627200,648000,681472,720000,762048,778752,790272

%N Intersection of A001694 and A195069.

%C Powerful(1) numbers k such that A046660(k) = 10.

%C These are the "primitive" members of A195069, in the sense that A195059 is the set of numbers k*m where k is in this sequence and m is squarefree and coprime to k.

%H Robert Israel, <a href="/A316499/b316499.txt">Table of n, a(n) for n = 1..2528</a>

%e a(3)=13824 is a member because 13824= 2^9*3^3, 9 and 3 are both greater than 1 and (9-1)+(3-1)=10.

%p N:= 10^6: # to get all terms <= N

%p p:= 1:

%p for i from 1 to 10 do F[i]:= {} od:

%p do

%p   p:= nextprime(p);

%p   if p^2 > N then break fi;

%p   for i from min(10,floor(log[p](N))-1) to 2 by -1 do F[i]:= F[i] union

%p     select(`<=`,`union`({p^(i+1)},seq(map(t -> p^(i+1-j)*t, F[j]),j=1..i-1)),N)

%p   od;

%p   F[1]:= F[1] union {p^2};

%p od:

%p sort(convert(F[10],list));

%Y Cf. A001694, A046660, A195069.

%K nonn

%O 1,1

%A _Robert Israel_, Jul 04 2018