Numbers n such that max(sfp(n), sfp(n+1), sfp(n+2)) < n^(1/3), where spf(n) is the squarefree part of n.
48, 629693, 8388223, 9841094
1
Rouse and Yang prove that for the exponent 1/3 there are an infinite number of these terms. This is not true for smaller exponents. The first 4 terms are the 25 numbers listed in the table in section 5 of the Rouse paper; the authors do not mention this sequence. There are no additional terms less than 10^9.
T. D. Noe, Plot of 4 terms
Jeremy Rouse and Yilin Yang, Three Consecutive Almost Squares, arXiv 1502.00605 (Feb 02 2015).
Eric W. Weisstein, MathWorld: Squarefree Part
(Mma) sfp[n_] := Module[{p, e}, {p, e} = Transpose[FactorInteger[n]]; Times @@ (p^Mod[e, 2])]; Select[Range[10^6], Max[sfp[#], sfp[# + 1], sfp[# + 2]] <= #^(1/3) &]
nonn,more,hard,nice
T. D. Noe, Feb 04 2015