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A081221 Number of consecutive numbers >= n having at least one square divisor > 1. 3

%I

%S 0,0,0,1,0,0,0,2,1,0,0,1,0,0,0,1,0,1,0,1,0,0,0,2,1,0,2,1,0,0,0,1,0,0,

%T 0,1,0,0,0,1,0,0,0,2,1,0,0,3,2,1,0,1,0,1,0,1,0,0,0,1,0,0,2,1,0,0,0,1,

%U 0,0,0,1,0,0,2,1,0,0,0,2,1,0,0,1,0,0,0,1,0,1,0,1,0,0,0,1,0,3,2,1,0,0,0,1,0

%N Number of consecutive numbers >= n having at least one square divisor > 1.

%C The first time terms 0..7 occur is at n = 1, 4, 8, 48, 242, 844, 22020, 217070. - _Antti Karttunen_, Sep 22 2017

%H Antti Karttunen, <a href="/A081221/b081221.txt">Table of n, a(n) for n = 1..65537</a>

%F mu(k) = 0 for n <= k < n+a(n) and mu(n+a(n)) <> 0, where mu = A008683 (Moebius function).

%F a(n)*mu(n) = 0.

%F a(A068781(n)) > 0.

%e For n = 3, 3 is a squarefree number, thus a(3) = 0.

%e For n = 48, neither 48 = 2^4 * 3 nor 49 = 7^2, nor 50 = 2^2 * 5 are squarefree, but 51 = 3*17 is, thus a(48) = 3. - _Antti Karttunen_, Sep 22 2017

%t Flatten@ Map[If[First@ # == 0, #, Reverse@ Range@ Length@ #] &, SplitBy[Table[DivisorSum[n, 1 &, And[# > 1, IntegerQ@ Sqrt@ #] &], {n, 120}], # > 0 &]] (* _Michael De Vlieger_, Sep 22 2017 *)

%o (PARI) A081221(n) = { my(k=0); while(!issquarefree(n+k),k++); k; }; \\ _Antti Karttunen_, Sep 22 2017

%Y Cf. A005117, A008683, A068781, A080733.

%K nonn

%O 1,8

%A _Reinhard Zumkeller_, Mar 10 2003

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Last modified February 18 04:48 EST 2020. Contains 332011 sequences. (Running on oeis4.)