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A362594
Exponentially odd numbers that are neither squarefree nor prime powers.
2
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
1,1
COMMENTS
The asymptotic density of this sequence is A065463 - A059956 = 0.09651509914... . - Amiram Eldar, Sep 27 2023
LINKS
FORMULA
This sequence is A126706 INTERSECT A268335.
A268335 = Union(S, T) where S is this sequence and T = {A005117 U A097054} = {A005117 U A246551}.
EXAMPLE
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.
MATHEMATICA
Select[Select[Range[1000], Nor[SquareFreeQ[#], PrimePowerQ[#]] &], Times @@ FactorInteger[#][[All, 1]] == (Sqrt[#] /. (c_ : 1)*a_^(b_ : 0) :> (c*a^b)^2) &]
KEYWORD
nonn
AUTHOR
Michael De Vlieger, Sep 08 2023
STATUS
approved