A362594 Exponentially odd numbers that are neither squarefree nor prime powers.

24, 40, 54, 56, 88, 96, 104, 120, 135, 136, 152, 160, 168, 184, 189, 216, 224, 232, 248, 250, 264, 270, 280, 296, 297, 312, 328, 344, 351, 352, 375, 376, 378, 384, 408, 416, 424, 440, 456, 459, 472, 480, 486, 488, 513, 520, 536, 544, 552, 568, 584, 594, 608, 616

Offset: 1

Author

Michael De Vlieger, Sep 08 2023

Keywords

• nonn

Comments

The asymptotic density of this sequence is A065463 - A059956 = 0.09651509914... . - Amiram Eldar, Sep 27 2023

Examples

			24 = 2^3 * 3^1 is in this sequence because it has 2 distinct prime factors whose multiplicities are odd and one such multiplicity exceeds 1.
		

Links

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

Crossrefs

Cf. A005117, A097054, A126706, A246551, A268335, A301517.

Cf. A059956, A065463.

Programs

Mathematica

Select[Select[Range[1000], Nor[SquareFreeQ[#], PrimePowerQ[#]] &], Times @@ FactorInteger[#][[All, 1]] == (Sqrt[#] /. (c_ : 1)*a_^(b_ : 0) :> (c*a^b)^2) &]

Formula

This sequence is A126706 INTERSECT A268335.

A268335 = Union(S, T) where S is this sequence and T = {A005117 U A097054} = {A005117 U A246551}.