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

1,1

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

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

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

Subsequence of A328014 and A348119.

Cf. A001694.

Sequence in context: A211766 A187164 A110275 * A160335 A019558 A339761

Adjacent sequences: A348117 A348118 A348119 * A348121 A348122 A348123

Keyword

nonn

Author

Amiram Eldar, Oct 01 2021

Status

approved