A348120 Starts of runs of 3 consecutive numbers whose powerful part is larger than their powerfree part (A328014).

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

Offset: 1

Author

Amiram Eldar, Oct 01 2021

Keywords

• nonn

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.

Examples

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

Links

• Amiram Eldar, Table of n, a(n) for n = 1..280

Crossrefs

Subsequence of A328014 and A348119.

Cf. A001694.

Programs

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