A049535 Starts of runs of exactly 6 consecutive nonsquarefree numbers.

22020, 24647, 30923, 47672, 55447, 57120, 73447, 74848, 96675, 105772, 121667, 121847, 152339, 171348, 179972, 182347, 185247, 190447, 200848, 204323, 215303, 229172, 233223, 234375, 240424, 268223, 274547, 310120, 327424, 338920

Offset: 1

Author

Labos Elemer

Keywords

• nonn

Examples

			Squares dividing the numbers in the starting at 22020 are 4, 361, 121, 9, 4, 25, respectively.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..1000

Crossrefs

The smallest members of such strings of length k are listed in A045882.

Cf. A001694 powerful numbers, A013929 not squarefree.

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).

Programs

Maple

Res:= NULL:
st:= 0:
for n from 1 to 500000 do
  if numtheory:-issqrfree(n) then
    if st = 6 then Res:= Res, n-6 fi;
    st:= 0;
  else
    st:= st+1;
  fi
od:
Res; # Robert Israel, Feb 08 2017

Mathematica

Select[Range[400000], !SquareFreeQ[#] && !SquareFreeQ[#+1] && !SquareFreeQ[#+2] && !SquareFreeQ[#+3] && !SquareFreeQ[#+4] && !SquareFreeQ[#+5] && SquareFreeQ[#+6]&] (* Vladimir Joseph Stephan Orlovsky, Mar 30 2011 *)
Flatten[Position[Partition[SquareFreeQ/@Range[60000],6,1],?(Union[#] == {False}&),{1},Heads->False]] (* _Harvey P. Dale, May 24 2014 *)

Formula

{ A078144(k) | A078144(k+1) = A078144(k)+1 and A078144(k+2) > A078144(k)+2 }. - M. F. Hasler, Feb 01 2016

Extensions

Definition corrected by Donald S. McDonald, Nov 07 2002

Corrected by Robert Israel, Feb 08 2017