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A049535 Starts of runs of exactly 6 consecutive nonsquarefree numbers.

%I A049535 #41 May 31 2024 22:11:14
%S A049535 22020,24647,30923,47672,55447,57120,73447,74848,96675,105772,121667,
%T A049535 121847,152339,171348,179972,182347,185247,190447,200848,204323,
%U A049535 215303,229172,233223,234375,240424,268223,274547,310120,327424,338920
%N A049535 Starts of runs of exactly 6 consecutive nonsquarefree numbers.
%H A049535 Robert Israel, <a href="/A049535/b049535.txt">Table of n, a(n) for n = 1..1000</a>
%F A049535 { A078144(k) | A078144(k+1) = A078144(k)+1 and A078144(k+2) > A078144(k)+2 }. - _M. F. Hasler_, Feb 01 2016
%e A049535 Squares dividing the numbers in the starting at 22020 are 4, 361, 121, 9, 4, 25, respectively.
%p A049535 Res:= NULL:
%p A049535 st:= 0:
%p A049535 for n from 1 to 500000 do
%p A049535   if numtheory:-issqrfree(n) then
%p A049535     if st = 6 then Res:= Res, n-6 fi;
%p A049535     st:= 0;
%p A049535   else
%p A049535     st:= st+1;
%p A049535   fi
%p A049535 od:
%p A049535 Res; # _Robert Israel_, Feb 08 2017
%t A049535 Select[Range[400000], !SquareFreeQ[#] && !SquareFreeQ[#+1] && !SquareFreeQ[#+2] && !SquareFreeQ[#+3] && !SquareFreeQ[#+4] && !SquareFreeQ[#+5] && SquareFreeQ[#+6]&] (* _Vladimir Joseph Stephan Orlovsky_, Mar 30 2011 *)
%t A049535 Flatten[Position[Partition[SquareFreeQ/@Range[60000],6,1],_?(Union[#] == {False}&),{1},Heads->False]] (* _Harvey P. Dale_, May 24 2014 *)
%Y A049535 The smallest members of such strings of length k are listed in A045882.
%Y A049535 Cf. A001694 powerful numbers, A013929 not squarefree.
%Y A049535 Cf. A045882 (min terms), A068781 (2-chains), A070258 (3-chains), A070284 (4-chains), A078144 (5-chains), A049535 (6-chains), A077640 (7-chains), A077647 (8-chains), A078143 (9-chains), A268313 (10-chains), A268314 (11-chains).
%K A049535 nonn
%O A049535 1,1
%A A049535 _Labos Elemer_
%E A049535 Definition corrected by _Donald S. McDonald_, Nov 07 2002
%E A049535 Corrected by _Robert Israel_, Feb 08 2017