A384418 Powerful exponentially squarefree numbers.

1, 4, 8, 9, 25, 27, 32, 36, 49, 64, 72, 100, 108, 121, 125, 128, 169, 196, 200, 216, 225, 243, 288, 289, 343, 361, 392, 441, 484, 500, 529, 576, 675, 676, 729, 800, 841, 864, 900, 961, 968, 972, 1000, 1024, 1089, 1125, 1152, 1156, 1225, 1323, 1331, 1352, 1369

Offset

1,2

Comments

Numbers having only squarefree exponents larger than 1 in their canonical prime factorization.

Links

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

Formula

Sum_{n>=1} 1/a(n) = Product_{p prime} (1 + Sum_{k>=2} 1/p^A005117(k)) = 1.83094143519375852659... .

Mathematica

seq[lim_] := Select[Union[Flatten[Table[i^2*j^3, {j, 1, Surd[lim, 3]}, {i, 1, Sqrt[lim/j^3]}]]], AllTrue[FactorInteger[#][[;; , 2]], SquareFreeQ] &]; seq[2000]

Crossrefs

Intersection of A001694 and A209061.

A383211 is the subsequence of prime powers (intersection of A246547 and this sequence).

Cf. A005117.

Sequence in context: A063907 A261987 A158340 * A350014 A259183 A383105

Adjacent sequences: A384415 A384416 A384417 * A384419 A384420 A384421

Keyword

nonn,easy

Author

Amiram Eldar, May 28 2025

Status

approved