OFFSET
1,2
COMMENTS
This sequence is infinite since the asymptotic density of the cubefull numbers is 0.
The corresponding record gaps are 7, 8, 16, 49, 47, 215, 169, 217, 135, 160, ... .
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000
EXAMPLE
The sequence of cubefull numbers begins with 1, 8, 16, 27, 32, 64, 81 and 125. The differences between these terms are 7, 8, 11, 5, 32, 17 and 44. The record values, 7, 8, 11, 32 and 44 occur after the cubefull numbers 1, 8, 16, 32 and 81, the first 5 terms of this sequence.
MATHEMATICA
cubQ[n_] := Min[FactorInteger[n][[;; , 2]]] > 2; seq[kmax_] := Module[{s = {}, k1 = 1, gapmax = 0, gap}, Do[If[cubQ[k], gap = k - k1; If[gap > gapmax, gapmax = gap; AppendTo[s, k1]]; k1 = k], {k, 2, kmax}]; s]; seq[10^6]
PROG
(PARI) iscubefull(n) = n==1 || vecmin(factor(n)[, 2]) > 2;
lista(kmax) = {my(gapmax = 0, gap, k1 = 1); for(k = 2, kmax, if(iscubefull(k), gap = k - k1; if(gap > gapmax, gapmax = gap; print1(k1, ", ")); k1 = k)); }
CROSSREFS
KEYWORD
nonn
AUTHOR
Amiram Eldar, May 13 2023
STATUS
approved