A077647 Smallest term of a run of at least 8 consecutive integers which are not squarefree.

1092747, 7216618, 8870024, 8870025, 14379271, 22635347, 24816974, 25047846, 33678771, 33908368, 33908369, 34394371, 34682346, 37923938, 49250144, 49250145, 53379270, 69147868, 69147869, 70918820, 70918821, 71927247, 72913022, 83605071, 85972019, 90571646

Offset: 1

Author

Labos Elemer, Nov 18 2002

Keywords

• nonn

Examples

			n=8870024: squares dividing n+j (j=0...8) i.e. 9 consecutive integers are as follows {4,25,121,841,4,49,961,9,16}
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A013929, A051681.

Cf. A045882 (first k-chain), 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

Mathematica

s8[x_] := Apply[Plus, Table[Abs[MoebiusMu[x+j]], {j, 0, 7}]]; Do[If[s8[n] == 0, Print[n]], {n, 10^8}]
Flatten[Position[Partition[SquareFreeQ/@Range[91000000],8,1],_?(Union[#]=={False}&),{1},Heads->False]]

PARI

for(n=1,10^8,forstep(k=7,0,-1,issquarefree(n+k)&&(n+=k)&&next(2));print1(n",")) \\ M. F. Hasler, Feb 03 2016

Formula

A077647 = { A077640[k] | A077640[k+1] = A077640[k]+1 }. - M. F. Hasler, Feb 01 2016