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A338388
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Numbers k such that there is a single biquadratefree powerful number (A338325) between k^2 and (k+1)^2.
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7
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2, 5, 8, 10, 11, 18, 19, 22, 25, 33, 37, 42, 46, 48, 51, 52, 53, 55, 57, 58, 59, 65, 70, 73, 78, 87, 88, 92, 94, 96, 102, 103, 104, 109, 111, 114, 115, 116, 119, 121, 122, 135, 144, 145, 149, 150, 155, 157, 164, 165, 166, 176, 181, 182, 183, 185, 190, 191, 195
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OFFSET
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1,1
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COMMENTS
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The asymptotic density of this sequence is 0.308276695... (Dehkordi, 1998).
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LINKS
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EXAMPLE
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2 is a term since there is a single biquadratefree powerful number, 8 = 2^3, between 2^2 = 4 and (2+1)^2 = 9.
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MATHEMATICA
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bqfpowQ[n_] := AllTrue[FactorInteger[n][[;; , 2]], MemberQ[{2, 3}, #] &]; Select[Range[200], Count[Range[#^2 + 1, (# + 1)^2 - 1], _?bqfpowQ] == 1 &]
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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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