A391140 Powerful terms in A339983.

108, 216, 432, 864, 972, 1000, 1728, 1944, 2000, 2744, 3456, 3888, 4000, 5488, 6912, 7776, 8000, 8748, 10976, 13500, 13824, 15552, 16000, 17496, 21296, 21952, 25000, 27000, 27648, 31104, 32000, 34992, 35152, 37044, 42592, 43904, 50000, 54000, 55296, 62208, 64000

Offset

1,1

Comments

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.

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.

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

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Mathematica

pows[max_] := Union[Flatten[Table[i^2*j^3, {j, 1, Surd[max, 3]}, {i, 1, Sqrt[max/j^3]}]]];
seq[max_] := Select[pows[max], q]; seq[64000] (* using the function "q" from A339983 *)

Crossrefs

Intersection of A001694 and A339983.

Cf. A005117.

Similar sequences: A391138, A391139, A391141.

Sequence in context: A044721 A095050 A339983 * A275996 A235292 A202202

Adjacent sequences: A391137 A391138 A391139 * A391141 A391142 A391143

Keyword

nonn

Author

Amiram Eldar, Dec 01 2025

Status

approved