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A371189
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The smaller of a pair of successive cubefull numbers without a powerful number between them.
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1
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27, 125, 243, 625, 1000, 1944, 2187, 3375, 4000, 4913, 10000, 15552, 16807, 17496, 27648, 34992, 50625, 83349, 107811, 139968, 157216, 194481, 250000, 279841, 389017, 390224, 405000, 614125, 628864, 810000, 970299, 1366875, 1372000, 1874048, 2000000, 2238728, 2248091
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OFFSET
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1,1
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LINKS
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EXAMPLE
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27 = 3^3 is a term since it is cubefull, and the next powerful number, 32 = 2^5, is also cubefull.
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MATHEMATICA
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cubQ[n_] := n == 1 || AllTrue[FactorInteger[n][[;; , 2]], # > 2 &];
seq[max_] := Module[{pows = Union[Flatten[Table[i^2*j^3, {j, 1, Surd[max, 3]}, {i, 1, Sqrt[max/j^3]}]]], ind = {}, d}, Do[If[cubQ[pows[[k]]], AppendTo[ind, k]], {k, 1, Length[pows]}]; d = Differences[ind]; pows[[ind[[Position[d, 1] // Flatten]]]]]; seq[10^6]
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PROG
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(PARI) iscubefull(n) = n == 1 || vecmin(factor(n)[, 2]) > 2;
lista(mx) = {my(s = List(), is1, is2); for(j = 1, sqrtnint(mx, 3), for(i = 1, sqrtint(mx\j^3), listput(s, i^2 * j^3))); s = Set(s); is1 = 1; for(i = 2, #s, is2 = iscubefull(s[i]); if(is1 && is2, print1(s[i-1], ", ")); is1 = is2); }
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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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