A396323 Numbers that are neither cubefree nor powerful with at least 3 distinct prime factors.

120, 168, 240, 264, 270, 280, 312, 336, 360, 378, 408, 440, 456, 480, 504, 520, 528, 540, 552, 560, 594, 600, 616, 624, 672, 680, 696, 702, 720, 728, 744, 750, 756, 760, 792, 810, 816, 840, 880, 888, 912, 918, 920, 936, 945, 952, 960, 984, 1008, 1026, 1032, 1040

Offset

1,1

Comments

Numbers in A391319 with at least 3 distinct prime factors.

Intersection of A000977 and A391319.

Intersection of A390949 and A391319.

Intersection of A000977, A046099, and A332785.

Smallest term with m distinct prime factors is 4*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    120 = 2^3 * 3 * 5
    2    168 = 2^3 * 3 * 7
    3    240 = 2^4 * 3 * 5
    4    264 = 2^3 * 3 * 11
    5    270 = 2 * 3^3 * 5
    6    280 = 2^3 * 5 * 7
    7    312 = 2^3 * 3 * 13
    8    336 = 2^4 * 3 * 7
    9    360 = 2^3 * 3^2 * 5
   38    840 = 2^3 * 3 * 5 * 7
   45    945 = 3^3 * 5 * 7
  855   9240 = 2^3 * 3 * 5 * 7 * 11

Mathematica

Select[Range[1200], And[Length[#] > 2, MemberQ[#, 1], AnyTrue[#, # > 2 &]] &[FactorInteger[#][[All, -1]] ] &]

Prog

(PARI) is(n) = my(f = factor(n)[, 2]~); #f >= 3 && vecmin(f) == 1 && vecmax(f) >= 3 \\ David A. Corneth, Jun 06 2026

Crossrefs

Cf. A000977, A002110, A013929, A046099, A126706, A332785, A375055, A378767, A390949, A391319, A391922, A396269.

Sequence in context: A099832 A111399 A030634 * A272594 A377156 A189975

Adjacent sequences: A396318 A396320 A396322 * A396324 A396325 A396326

Keyword

nonn,easy,new

Author

Michael De Vlieger, May 31 2026

Status

approved