A391319 Numbers that are neither cubefree nor powerful.

24, 40, 48, 54, 56, 80, 88, 96, 104, 112, 120, 135, 136, 152, 160, 162, 168, 176, 184, 189, 192, 208, 224, 232, 240, 248, 250, 264, 270, 272, 280, 296, 297, 304, 312, 320, 328, 336, 344, 351, 352, 360, 368, 375, 376, 378, 384, 405, 408, 416, 424, 440, 448, 456

Offset

1,1

Comments

Intersection of A046099 and A332785.

A332785 is the union of this sequence and A386684, disjoint subsets.

A378767 is the union of this sequence and A372404, disjoint subsets.

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    80 = 2^4 * 5
  7    88 = 2^3 * 11
 11   120 = 2^3 * 3 * 5
 12   135 = 3^3 * 5
 17   168 = 2^3 * 3 * 7
 76   600 = 2^3 * 3 * 5^2
111   840 = 2^3 * 3 * 5 * 7

Mathematica

fQ[x_] := And[MemberQ[#, 1], AnyTrue[#, # > 2 &]] &[FactorInteger[x][[;; , -1]] ]; Select[Range[500], fQ]

Crossrefs

Cf. A013929, A024619, A046099, A052485, A126706, A332785, A372404, A378767, A386684.

Sequence in context: A378767 A362148 A391415 * A382879 A391922 A062374

Adjacent sequences: A391316 A391317 A391318 * A391320 A391321 A391322

Keyword

nonn

Author

Michael De Vlieger, Dec 07 2025

Status

approved