%I #5 Sep 26 2022 20:15:28
%S 1,2,6,10,15,22,68,153,174,615,656,1422,1711,1846,2425,7164,8791,
%T 13988,42755,48290,186108,221131,3860731
%N Starts of record-length runs of consecutive positive integers with the same value of A071626.
%C The corresponding record lengths are 1, 2, 4, 5, 7, 11, 17, 21, 29, 30, 32, 33, 35, 52, 57, 64, 78, 86, 96, 113, 122, 208, 221, ...
%C The common values of A071626 in each run are 0, 1, 3, 4, 5, 6, 10, 14, 15, 26, 27, 38, 40, 42, 48, 77, 84, 103, 172, 182, 335, 365, 1338, ...
%F 2 is a term since it starts a run of 2 consecutive integers with the same value of A071626: A071626(2) = A071626(3) = 1.
%F 6 is the next term since it starts a run of 4 consecutive integers with the same value of A071626: A071626(6) = A071626(7) = A071626(8) = A071626(9) = 3.
%t s[n_] := Length[Union[FactorInteger[n!][[;; , 2]]]]; s[1] = 0; ind = Position[Differences[Table[s[n], {n, 1, 1000}]], _?(# != 0 &)] // Flatten; d = Differences[ind]; seq = {1}; dm = -1; Do[If[d[[i]] > dm, dm = d[[i]]; AppendTo[seq, ind[[i]] + 1]], {i, 1, Length[d]}]; seq
%Y Cf. A071626, A357385, A357386.
%K nonn,more
%O 1,2
%A _Amiram Eldar_, Sep 26 2022