A391283 Primitive exponential admirable numbers: the powerful terms in A336680.

900, 1764, 4356, 4500, 4900, 6084, 7056, 10404, 12348, 12996, 19044, 30276, 34596, 47916, 49284, 60516, 66564, 79092, 79524, 88200, 101124, 112500, 125316, 132300, 133956, 161604, 176868, 181476, 191844, 217800, 224676, 246924, 248004, 285156, 304200, 326700, 338724

Offset

1,1

Comments

If k is a term, then k*m is a term in A336680 for any squarefree number m that is coprime to k.

Any term in A336680 is of the form k*m where k is a term in this sequence and m is a squarefree number coprime to k. Therefore, A336680 can be generated from this sequence by multiplying with coprime squarefree numbers, and the asymptotic density of A336680 can be evaluated from the terms in this sequence (see the Comments section of A336680).

The least odd term is a(2513) = A391284(1) = 6485886225.

If k is a unitary admirable number (A328328) that is squarefree, then k^2 is a term (and conversely, if k^2 is a term and k is squarefree, then k is in A328328). There are terms that are not squares of squarefree numbers, e.g., 4500, 12348, 47916, ... .

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], expAdmQ]; seq[400000] (* using the function "expAdmQ" from A336680 *)

Crossrefs

Intersection of A001694 and A336680.

A391284 is a subsequence.

Cf. A005117, A328328.

Sequence in context: A336680 A383693 A383697 * A383694 A383698 A386798

Adjacent sequences: A391280 A391281 A391282 * A391284 A391285 A391286

Keyword

nonn

Author

Amiram Eldar, Dec 05 2025

Status

approved