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

1,1

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.

Links

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

Example

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.

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));

Crossrefs

Cf. A001694, A046660, A195069.

Sequence in context: A234881 A220584 A195069 * A135290 A204837 A351162

Adjacent sequences: A316496 A316497 A316498 * A316500 A316501 A316502

Keyword

nonn

Author

Robert Israel, Jul 04 2018

Status

approved