A371186 Indices of the cubes in the sequence of cubefull numbers.
1, 2, 4, 6, 8, 10, 13, 15, 18, 20, 23, 24, 29, 32, 34, 38, 39, 43, 45, 48, 50, 54, 57, 58, 61, 67, 69, 73, 75, 77, 81, 85, 88, 90, 94, 96, 99, 102, 105, 107, 110, 113, 117, 124, 126, 128, 130, 135, 137, 139, 143, 147, 149, 153, 158, 160, 163, 167, 169, 172, 176
Offset: 1
Examples
The first 4 cubefull numbers are 1, 8, 16, and 27. The 1st, 2nd, and 4th, 1, 8, and 27, are the first 3 cubes. Therefore, the first 3 terms of this sequence are 1, 2, and 4.
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Programs
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Mathematica
cubQ[n_] := n == 1 || AllTrue[FactorInteger[n], Last[#] >= 3 &]; Position[Select[Range[10^6], cubQ], _?(IntegerQ[Surd[#1, 3]] &)] // Flatten (* or *) seq[max_] := Module[{cubs = Union[Flatten[Table[i^5*j^4*k^3, {i, 1, Surd[max, 5]}, {j, 1, Surd[max/i^5, 4]}, {k, Surd[max/(i^5*j^4), 3]}]]], s = {}}, Do[If[IntegerQ[Surd[cubs[[k]], 3]], AppendTo[s, k]], {k, 1, Length[cubs]}]; s]; seq[10^6] -
PARI
iscub(n) = n == 1 || vecmin(factor(n)[, 2]) >= 3; lista(kmax) = {my(f, c = 0); for(k = 1, kmax, if(iscub(k), c++; if(ispower(k, 3), print1(c, ", "))));}
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