%I #9 Sep 28 2022 03:53:07
%S 1,2,116,6,10,290,15,333,136,55,22,102,410,119,477,232,68,261,451,
%T 2343,153,348,708,492,1037,377,976,826,174,615,1940,656,1422,8642,
%U 1711,7712,10382,3232,5921,9089,3434,2286,2556,1988,5617,6040,6576,17025,12939,6194,19694
%N a(n) is the start of the least run of exactly n consecutive positive integers with the same value of A071626, or -1 if no such run exists.
%C The common values of A071626 in each run are 0, 1, 12, 3, 4, 18, 5, 20, 13, 9, 6, 12, 22, 13, 23, 17, 10, 18, 23, ...
%H Amiram Eldar, <a href="/A357386/b357386.txt">Table of n, a(n) for n = 1..162</a>
%e a(2) = 2 since A071626(2) = A071626(3) = 1, A071626(1) = 0 and A071626(4) = 2.
%e a(3) = 116 since A071626(116) = A071626(117) = A071626(118) = 12, A071626(115) = 11 and A071626(119) = 13, and 116 is the least integer with this property.
%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}; Do[i = FirstPosition[d, k]; If[MissingQ[i], Break[]]; AppendTo[seq, ind[[i[[1]]]] + 1], {k, 2, Max[d]}]; seq
%Y Cf. A071626, A357385, A357387.
%K nonn
%O 1,2
%A _Amiram Eldar_, Sep 26 2022