A396269 Cubefree k that are neither squarefree nor squareful that have more than 2 distinct prime factors.

60, 84, 90, 126, 132, 140, 150, 156, 180, 198, 204, 220, 228, 234, 252, 260, 276, 294, 300, 306, 308, 315, 340, 342, 348, 350, 364, 372, 380, 396, 414, 420, 444, 450, 460, 468, 476, 490, 492, 495, 516, 522, 525, 532, 550, 558, 564, 572, 580, 585, 588, 612, 620

Offset

1,1

Comments

Intersection of A004709 and A390949.

Intersection of A000977 and A386684.

Intersection of A386684 and A390949.

Intersection of A000977, A004709, and A332785.

Smallest term with m distinct prime factors is 2*A002110(m), m > 2.

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     60 = 2^2 * 3 * 5
    2     84 = 2^2 * 3 * 7
    3     90 = 2 * 3^2 * 5
    4    126 = 2 * 3^2 * 7
    5    132 = 2^2 * 3 * 11
    6    140 = 2^2 * 5 * 7
    7    150 = 2 * 3 * 5^2
    8    156 = 2^2 * 3 * 13
    9    180 = 2^2 * 3^2 * 5
   22    315 = 3^2 * 5 * 7
   32    420 = 2^2 * 3 * 5 * 7
  603   4620 = 2^2 * 3 * 5 * 7 * 11

Mathematica

Select[Range[2^10], And[Length[#] > 2, AnyTrue[#, # > 1 &], AllTrue[#, # < 3 &]] &[FactorInteger[#][[All, -1]] ] &]

Crossrefs

Cf. A000977, A002110, A004709, A013929, A054753, A126706, A332785, A375055, A386684, A390949, A391023, A396323.

Sequence in context: A379094 A009129 A174292 * A085987 A356413 A086974

Adjacent sequences: A396266 A396267 A396268 * A396270 A396271 A396272

Keyword

nonn,easy

Author

Michael De Vlieger, May 31 2026

Status

approved