A316499 Intersection of A001694 and A195069.

2048, 9216, 13824, 20736, 25600, 31104, 46656, 50176, 64000, 69984, 104976, 115200, 123904, 157464, 160000, 172800, 173056, 175616, 177147, 225792, 236196, 259200, 288000, 338688, 388800, 400000, 432000, 508032, 557568, 583200, 614656, 627200, 648000, 681472, 720000, 762048, 778752, 790272

Offset: 1

Author

Robert Israel, Jul 04 2018

Keywords

• nonn

Comments

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

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.

Examples

			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.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..2528

Crossrefs

Cf. A001694, A046660, A195069.

Programs

Maple

N:= 10^6: # to get all terms <= N
p:= 1:
for i from 1 to 10 do F[i]:= {} od:
do
  p:= nextprime(p);
  if p^2 > N then break fi;
  for i from min(10,floor(log[p](N))-1) to 2 by -1 do F[i]:= F[i] union
    select(`<=`,`union`({p^(i+1)},seq(map(t -> p^(i+1-j)*t, F[j]),j=1..i-1)),N)
  od;
  F[1]:= F[1] union {p^2};
od:
sort(convert(F[10],list));