A391140 - OEIS

%I #12 Mar 09 2026 09:44:35

%S 108,216,432,864,972,1000,1728,1944,2000,2744,3456,3888,4000,5488,

%T 6912,7776,8000,8748,10976,13500,13824,15552,16000,17496,21296,21952,

%U 25000,27000,27648,31104,32000,34992,35152,37044,42592,43904,50000,54000,55296,62208,64000

%N Powerful terms in A339983.

%C These are a primitive terms in A339983: If k is a term and m is a squarefree number coprime to k, then k*m is a term in A339983.

%C Most of the terms in A339983 can be generated from this sequence by multiplying terms with coprime squarefree numbers, but there are also terms that can be generated from A391141.

%C The asymptotic density of A339983 can be evaluated from the terms in these two sequences (see the Comments section of A339983).

%H Amiram Eldar, <a href="/A391140/b391140.txt">Table of n, a(n) for n = 1..10000</a>

%t pows[max_] := Union[Flatten[Table[i^2*j^3, {j, 1, Surd[max, 3]}, {i, 1, Sqrt[max/j^3]}]]];

%t seq[max_] := Select[pows[max], q]; seq[64000] (* using the function "q" from A339983 *)

%Y Intersection of A001694 and A339983.

%Y Cf. A005117.

%Y Similar sequences: A391138, A391139, A391141.

%K nonn

%O 1,1

%A _Amiram Eldar_, Dec 01 2025