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A081221 Number of consecutive numbers >= n having at least one square divisor > 1. 3
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, 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, 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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,8

COMMENTS

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

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..65537

FORMULA

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

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

a(A068781(n)) > 0.

EXAMPLE

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

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

MATHEMATICA

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 *)

PROG

(PARI) A081221(n) = { my(k=0); while(!issquarefree(n+k), k++); k; }; \\ Antti Karttunen, Sep 22 2017

CROSSREFS

Cf. A005117, A008683, A068781, A080733.

Sequence in context: A304685 A186714 A160382 * A280827 A103840 A066301

Adjacent sequences:  A081218 A081219 A081220 * A081222 A081223 A081224

KEYWORD

nonn

AUTHOR

Reinhard Zumkeller, Mar 10 2003

STATUS

approved

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Last modified January 19 20:41 EST 2020. Contains 331066 sequences. (Running on oeis4.)