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A338326
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The number of biquadratefree powerful numbers (A338325) between the consecutive squares n^2 and (n+1)^2.
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8
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0, 1, 0, 0, 1, 0, 0, 1, 0, 1, 1, 0, 0, 2, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 2, 0, 1, 0, 0, 3, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 1, 1, 1, 0, 1, 0, 1, 1, 1, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 1, 0, 2, 1, 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 0, 0, 0, 1
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OFFSET
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1,14
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COMMENTS
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Dehkordi (1998) proved that for each k>=0 the sequence of numbers m such that a(m) = k has a positive asymptotic density.
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LINKS
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EXAMPLE
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a(2) = 1 since there is one biquadratefree powerful number, 8 = 2^3, between 2^2 = 4 and 3^2 = 9.
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MATHEMATICA
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bqfpowQ[n_] := AllTrue[FactorInteger[n][[;; , 2]], MemberQ[{2, 3 }, #] &]; a[n_] := Count[Range[n^2 + 1, (n + 1)^2 - 1], _?bqfpowQ]; Array[a, 100]
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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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