

A348120


Starts of runs of 3 consecutive numbers whose powerful part is larger than their powerfree part (A328014).


2



48, 350, 9800, 11374, 31211, 32798, 48373, 59534, 63000, 103246, 118579, 373827, 488187, 625974, 629693, 830464, 1193983, 1294298, 2989439, 3815174, 4231248, 5132699, 5331248, 6674166, 7616950, 7970157, 8388223, 8670375, 9235520, 9516680, 9841094, 11121382, 12708359
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OFFSET

1,1


COMMENTS

There are no runs of 4 consecutive numbers below 10^10.
It is conjectured that there are no runs of 3 consecutive numbers that are powerful (A001694), but if they do exist, their starts are contained in this sequence.


LINKS



EXAMPLE

48 is a term since 48, 49 and 50 are all in A328014.


MATHEMATICA

f[p_, e_] := If[e==1, p, 1]; s[n_] := Times @@ (f @@@ FactorInteger[n]); q[n_] := s[n]^2 < n; v = q /@ Range[3]; seq = {}; Do[v = Append[Drop[v, 1], q[k]]; If[And @@ v, AppendTo[seq, k  2]], {k, 4, 10^6}]; seq


CROSSREFS



KEYWORD

nonn


AUTHOR



STATUS

approved



