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A132953
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a(n) = the sum of the isolated totatives of n.
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1
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0, 1, 0, 4, 0, 6, 0, 16, 0, 20, 0, 24, 0, 42, 15, 64, 0, 54, 0, 80, 21, 110, 0, 96, 0, 156, 0, 168, 0, 120, 0, 256, 33, 272, 35, 216, 0, 342, 39, 320, 0, 252, 0, 440, 135, 506, 0, 384, 0, 500, 51, 624, 0, 486, 55, 672, 57, 812, 0, 480, 0, 930, 189, 1024, 65, 660, 0, 1088, 69
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OFFSET
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1,4
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COMMENTS
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An isolated totative, k, of n is a positive integer which is coprime to n, is <= n and is such that neither (k-1) nor (k+1) are coprime to n.
a(2n) = phi(2n)*n, where phi(n) = A000010(n).
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LINKS
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Table of n, a(n) for n=1..69.
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FORMULA
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a(n)=n/2*A132952(n). - Robert G. Wilson v, Sep 13 2007.
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EXAMPLE
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The positive integers which are <= 15 and are coprime to 15 are 1,2,4,7,8,11,13,14. Of these, 1 and 2 are adjacent, 7 and 8 are adjacent and 13 and 14 are adjacent. So the isolated totatives of 15 are 4 and 11. Therefore a(15) = 4 + 11 = 15.
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MATHEMATICA
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fQ[k_, n_] := GCD[k, n] == 1 && GCD[k - 1, n] > 1 && GCD[k + 1, n] > 1; f[n_] := Plus @@ Select[ Rest[ Range@n - 1], fQ[ #, n] &]; Array[f, 69] (* Robert G. Wilson v *)
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CROSSREFS
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Cf. A132952.
Sequence in context: A163407 A023891 A075091 * A195207 A157721 A085968
Adjacent sequences: A132950 A132951 A132952 * A132954 A132955 A132956
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KEYWORD
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nonn
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AUTHOR
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Leroy Quet Sep 05 2007
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EXTENSIONS
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Edited and extended by Robert G. Wilson v, Sep 13 2007
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STATUS
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approved
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