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A080733
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Smallest distance from n to a squarefree number.
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5
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0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 1, 1, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 1, 2, 1, 0, 1, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 2, 1, 0, 0, 0, 1, 0
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OFFSET
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1,49
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COMMENTS
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a(n) = min (abs(n-k) : where k runs through the squarefree numbers ).
The sequence is unbounded.
The first 0 occurs at 1, the first 1 at 4, the first 2 at 49, the first 3 at 846. - Antti Karttunen, Sep 22 2017
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LINKS
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Antti Karttunen, Table of n, a(n) for n = 1..65537
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FORMULA
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a(A005117(n)) = 0.
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EXAMPLE
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For n = 3, 3 itself is a squarefree number, thus a(3) = 0.
For n = 48, 48 = 2^4 * 3 is not squarefree, 49 = 7^2 is not squarefree, but 47 is, thus a(48) = abs(48-47) = 1.
For n = 49, neither 49 = 7^2, nor 48 = 2^4 * 3 nor 50 = 2^2 * 5 is squarefree, while both 47 and 51 are, thus a(49) = abs(49-47) = abs(49-51) = 2.
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MATHEMATICA
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nn=110; With[{sqfr=Select[Range[nn+10], SquareFreeQ]}, Flatten[Table[ Union[ Abs[ Nearest[ sqfr, n]-n]], {n, nn}]]] (* Harvey P. Dale, Jun 01 2012 *)
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PROG
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(PARI) A080733(n) = { my(k=0); while((!issquarefree(n+k))&&(!issquarefree(n-k)), k++); k; }; \\ Antti Karttunen, Sep 22 2017
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CROSSREFS
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Cf. A051699.
Cf. A005117, A081221.
Sequence in context: A135929 A346377 A338757 * A080732 A301295 A215036
Adjacent sequences: A080730 A080731 A080732 * A080734 A080735 A080736
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KEYWORD
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nonn
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AUTHOR
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Benoit Cloitre, Mar 08 2003
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EXTENSIONS
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Examples added by Antti Karttunen, Sep 22 2017
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STATUS
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approved
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