A049535 - OEIS

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

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OFFSET

1,1

LINKS

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

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 the numbers in the starting at 22020 are 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;

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

Adjacent sequences: A049532 A049533 A049534 * A049536 A049537 A049538

KEYWORD

nonn

AUTHOR

Labos Elemer

EXTENSIONS

Definition corrected by Donald S. McDonald, Nov 07 2002

Corrected by Robert Israel, Feb 08 2017

STATUS

approved