A139703 Nonsquarefree positive integers k such that the largest prime power dividing k is prime.

20, 28, 44, 52, 60, 68, 76, 84, 88, 92, 99, 104, 116, 117, 124, 132, 136, 140, 148, 152, 153, 156, 164, 171, 172, 184, 188, 198, 204, 207, 212, 220, 228, 232, 234, 236, 244, 248, 260, 261, 264, 268, 272, 276, 279, 284, 292, 296, 304, 306, 308, 312, 316, 328

Offset: 1

Author

Leroy Quet, Jun 13 2008

Keywords

• nonn

Examples

			99 = 3^2 * 11^1. 99 is therefore not squarefree, because it is divisible by 3^2. Also, the largest prime power dividing 99 is 11^1. This is a prime, so 99 is included in the sequence.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Intersection of A013929 and A122144.

Programs

Maple

filter:= proc(n) local F,t,k;
  F:= ifactors(n)[2];
  if max(seq(t[2],t=F)) = 1 then return false fi;
  k:= max[index]([seq(t[1]^t[2],t=F)]);
  F[k,2]=1
end proc:
select(filter, [$2..1000]); # Robert Israel, Jan 31 2021

Mathematica

Select[Range[330], Max[(f = FactorInteger[#])[[;;, 2]]] > 1 && Max[Power @@@ f] == f[[-1, 1]] &] (* Amiram Eldar, Jun 26 2025 *)

Formula

This sequence consists of the nonsquarefree terms of A122144.

Extensions

Extended by Ray Chandler, Jul 01 2009