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A363082
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Numbers k neither squarefree nor prime power such that q*r > k, where q = A053669(k) is the smallest prime that does not divide k and r = A007947(k) is the squarefree kernel.
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4
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12, 18, 20, 24, 28, 44, 52, 60, 68, 76, 84, 90, 92, 116, 120, 124, 126, 132, 140, 148, 150, 156, 164, 168, 172, 180, 188, 198, 204, 212, 220, 228, 234, 236, 244, 260, 264, 268, 276, 284, 292, 306, 308, 312, 316, 332, 340, 342, 348, 356, 364, 372, 380, 388, 404, 408, 412, 414, 420
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OFFSET
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1,1
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LINKS
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Michael De Vlieger, Plot b(n) = A126706(n) at (x, y) for n = ym + x = 1..1032256, m = 1016 and x = 1..m, y = 0..m-1, showing b(n) in A360765 in white, and b(n) in this sequence in other colors, where red indicates b(n) also in A360767, and blue indicates b(n) also in A360768.
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FORMULA
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EXAMPLE
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a(1) = 12 since 12 is the smallest number that is neither squarefree nor a prime power. Additionally, 12 < 5*6.
a(2) = 18 since it is in A126706, and like 12, 18 < 5*6.
a(3) = 20 since it is neither squarefree nor prime power, and 20 < 3*10.
36 is not in this sequence since 36 > 5*6.
40 is not in this sequence since 40 > 3*10, etc.
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MATHEMATICA
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Select[Select[Range[452], Nor[PrimePowerQ[#], SquareFreeQ[#]] &], Function[{k, f}, Function[{q, r}, q r > k] @@ {SelectFirst[Prime@ Range[PrimePi[f[[-1, 1]]] + 1], ! Divisible[k, #] &], Times @@ f[[All, 1]]} ] @@ {#, FactorInteger[#]} &]
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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