A391922 Numbers that are neither cubefree nor powerful and have exactly 2 distinct prime factors.

24, 40, 48, 54, 56, 80, 88, 96, 104, 112, 135, 136, 152, 160, 162, 176, 184, 189, 192, 208, 224, 232, 248, 250, 272, 296, 297, 304, 320, 328, 344, 351, 352, 368, 375, 376, 384, 405, 416, 424, 448, 459, 464, 472, 486, 488, 496, 513, 536, 544, 567, 568, 584, 592

Offset

1,1

Comments

Numbers whose multiset of prime factor exponents is {1, m} with m > 2.

Numbers in A391319 with 2 distinct prime factors.

This sequence is A345381 \ A054753.

Intersection of A046099 and A345381.

Intersection of A007774 and A391319.

Intersection of A345381 and A391319.

Intersection of A007774, A046099, and A332785.

Links

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

Example

Table of n, a(n) for n = 1..12:
 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
 8    96 = 2^5 *  3
 9   104 = 2^3 * 13
10   112 = 2^4 *  7
11   135 = 3^3 *  5
12   136 = 2^3 * 17

Mathematica

Select[Range[600], And[Length[#] == 2, AnyTrue[#, # > 2 &], MemberQ[#, 1] ] &[FactorInteger[#][[All, -1]] ] &]

Crossrefs

Cf. A007774, A013929, A046099, A054753, A126706, A200511, A332785, A345381, A378767, A391319.

Sequence in context: A391415 A391319 A382879 * A062374 A272593 A048104

Adjacent sequences: A391919 A391920 A391921 * A391923 A391924 A391925

Keyword

nonn

Author

Michael De Vlieger, Dec 23 2025

Status

approved