A371189 The smaller of a pair of successive cubefull numbers without a powerful number between them.

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

Offset

1,1

Links

Amiram Eldar, Table of n, a(n) for n = 1..500

Index entries for sequences related to powerful numbers.

Example

27 = 3^3 is a term since it is cubefull, and the next powerful number, 32 = 2^5, is also cubefull.

Mathematica

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]

Prog

(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); }

Crossrefs

Cf. A001694, A036966.

Sequence in context: A179145 A369118 A118092 * A126272 A016755 A074100

Adjacent sequences: A371186 A371187 A371188 * A371190 A371191 A371192

Keyword

nonn

Author

Amiram Eldar, Mar 14 2024

Status

approved