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A337736
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The number of cubefull numbers (A036966) between the consecutive cubes n^3 and (n+1)^3.
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6
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0, 1, 1, 1, 1, 2, 1, 2, 1, 2, 0, 4, 2, 1, 3, 0, 3, 1, 2, 1, 3, 2, 0, 2, 5, 1, 3, 1, 1, 3, 3, 2, 1, 3, 1, 2, 2, 2, 1, 2, 2, 3, 6, 1, 1, 1, 4, 1, 1, 3, 3, 1, 3, 4, 1, 2, 3, 1, 2, 3, 2, 3, 2, 3, 3, 2, 1, 4, 2, 1, 1, 0, 7, 1, 1, 4, 3, 2, 2, 2, 3, 3, 2, 0, 4, 2, 4
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OFFSET
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1,6
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COMMENTS
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For each k >= 0 the sequence of solutions to a(x) = k has a positive asymptotic density (Shiu, 1991).
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LINKS
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FORMULA
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Asymptotic mean: lim_{m->oo} (1/m) Sum_{k=1..m} a(k) = A362974 - 1 = 3.659266... . - Amiram Eldar, May 11 2023
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EXAMPLE
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a(2) = 1 since there is one cubefull number, 16 = 2^4, between 2^3 = 8 and 3^3 = 27.
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MATHEMATICA
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cubQ[n_] := Min[FactorInteger[n][[;; , 2]]] > 2; a[n_] := Count[Range[n^3 + 1, (n + 1)^3 - 1], _?cubQ]; 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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