A390128 Biquadratefree numbers that are neither cubefree nor squareful.

24, 40, 54, 56, 88, 104, 120, 135, 136, 152, 168, 184, 189, 232, 248, 250, 264, 270, 280, 296, 297, 312, 328, 344, 351, 360, 375, 376, 378, 408, 424, 440, 456, 459, 472, 488, 504, 513, 520, 536, 540, 552, 568, 584, 594, 600, 616, 621, 632, 664, 680, 686, 696, 702

Offset

1,1

Comments

Intersection of A391319 and A046100 = A391319 \ A392360.

Numbers k whose smallest prime power factor exponent m = 1 and largest exponent M = 3.

A375076 is a proper subset that contains all terms in A360793; a(26) = 360 = 2^3 * 3^2 * 5 is not in A375076.

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    54 = 2   *  3^3
 4    56 = 2^3 *  7
 5    88 = 2^3 * 11
 6   104 = 2^3 * 13
 7   120 = 2^3 *  3   * 5
 8   135 = 3^3 *  5
 9   136 = 2^3 * 17
10   152 = 2^3 * 19
13   189 = 3^3 *  7
26   360 = 2^3 *  3^2 * 5

Mathematica

Select[Range[720], And[#1 == 1, #2 == 3] & @@ MinMax@ FactorInteger[#][[;; , -1]] &]

Crossrefs

Cf. A013929, A024619, A046099, A046100, A052485, A126706, A332785, A360793, A362148, A375076, A391497, A392360.

Sequence in context: A334801 A391497 A362594 * A360793 A375076 A297401

Adjacent sequences: A390125 A390126 A390127 * A390129 A390130 A390131

Keyword

nonn,easy

Author

Michael De Vlieger, Jan 27 2026

Status

approved