A391415 Nonsquarefree numbers that are neither cubefree nor perfect powers.

24, 40, 48, 54, 56, 72, 80, 88, 96, 104, 108, 112, 120, 135, 136, 152, 160, 162, 168, 176, 184, 189, 192, 200, 208, 224, 232, 240, 248, 250, 264, 270, 272, 280, 288, 296, 297, 304, 312, 320, 328, 336, 344, 351, 352, 360, 368, 375, 376, 378, 384, 392, 405, 408

Offset

1,1

Comments

A378767(16) = A362148(16) = 144, but 144 = 2^4 * 3^2 is a perfect power and is not in this sequence.

Links

Michael De Vlieger, Table of n, a(n) for n = 1..10000

Example

Table of n, a(n) for select n:
 n   a(n)
-----------------------
 1    24 = 2^3 *  3
 2    40 = 2^3 *  5
 3    48 = 2^4 *  3
 4    54 = 2   *  3^3
 5    56 = 2^3 *  7
 6    72 = 2^3 *  3^2
 7    80 = 2^4 *  5
 8    88 = 2^3 * 11
 9    96 = 2^5 *  3
13   120 = 2^3 *  3 * 5
14   135 = 3^3 *  5
19   168 = 2^3 *  3 * 7

Mathematica

fQ[x_] := And[Length[#] > 1, AnyTrue[#, # > 2 &], GCD @@ # == 1] &@ FactorInteger[x][[;; , -1]]; Select[Range[2^10], fQ]

Crossrefs

Cf. A024619, A126706.

Intersection of A007916, A013929, and A046099.

Union of A052486 (Achilles numbers) and A391319, disjoint subsets.

Intersection of A303946 and A046099 = A303946 \ A004709 = A362148 \ A389864 = A378767 \ A391416.

Sequence in context: A379336 A378767 A362148 * A391319 A382879 A391922

Adjacent sequences: A391412 A391413 A391414 * A391416 A391417 A391418

Keyword

nonn,easy

Author

Michael De Vlieger, Dec 13 2025

Status

approved