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A049535 Starts for strings of exactly 6 consecutive nonsquarefree numbers. 11
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
LINKS
FORMULA
{ A078144(k) | A078144(k+1) = A078144(k)+1 and A078144(k+2) > A078144(k)+2 }. - M. F. Hasler, Feb 01 2016
EXAMPLE
Squares dividing string started by 22020 are as follows: 4, 361, 121, 9, 4, 25, respectively.
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 *)
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).
Sequence in context: A203441 A217533 A045133 * A091459 A224574 A232861
KEYWORD
nonn
AUTHOR
EXTENSIONS
Definition corrected by Donald S. McDonald, Nov 07 2002
Corrected by Robert Israel, Feb 08 2017
STATUS
approved

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Last modified February 23 19:35 EST 2024. Contains 370283 sequences. (Running on oeis4.)