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A337737
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Least number k such that there are exactly n cubefull numbers between k^3 and (k+1)^3.
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2
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1, 2, 6, 15, 12, 25, 43, 73, 480, 1981, 3205, 9038, 16099, 376340, 211318, 2461230, 2253517, 16907618, 106308537, 312911063
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OFFSET
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0,2
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COMMENTS
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a(n) = least k such that A337736(k) = n.
Shiu (1991) proved that infinitely many values of k exist for every n. Therefore, this sequence is infinite.
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LINKS
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EXAMPLE
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a(0) = 1 since there are no cubefull numbers between 1^3 = 1 and 2^3 = 8.
a(1) = 2 since there is one cubefull number, 16 = 2^4, between 2^3 = 8 and 3^3 = 27.
a(2) = 6 since there are 2 cubefull numbers, 243 = 3^5 and 256 = 2^8, between 6^3 = 216 and 7^3 = 343.
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MATHEMATICA
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cubQ[n_] := Min[FactorInteger[n][[;; , 2]]] > 2; f[n_] := Count[Range[n^3 + 1, (n + 1)^3 - 1], _?cubQ]; mx = 8; s = Table[0, {mx}]; c = 0; n = 1; While[c < mx, i = f[n] + 1; If[i <= mx && s[[i]] == 0, c++; s[[i]] = n]; n++] ; s
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CROSSREFS
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KEYWORD
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nonn,more
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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