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A132952
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a(n) = number of isolated totatives of n.
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1
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0, 1, 0, 2, 0, 2, 0, 4, 0, 4, 0, 4, 0, 6, 2, 8, 0, 6, 0, 8, 2, 10, 0, 8, 0, 12, 0, 12, 0, 8, 0, 16, 2, 16, 2, 12, 0, 18, 2, 16, 0, 12, 0, 20, 6, 22, 0, 16, 0, 20, 2, 24, 0, 18, 2, 24, 2, 28, 0, 16, 0, 30, 6, 32, 2, 20, 0, 32, 2, 24, 0, 24, 0, 36, 10, 36, 2, 24, 0, 32, 0, 40, 0, 24, 2, 42, 2, 40, 0
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,4
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COMMENTS
| An isolated totative, k, of n is a positive integer which is less than and coprime to n and is such that neither (k-1) nor (k+1) are coprime to n.
a(2n) = phi(2n), where phi(n) = A000010(n).
If k is an isolated totative so is n-k. - Robert G. Wilson v, Sep 13 2007.
a(n)=0 for n's: A061345 "Odd prime powers". - Robert G. Wilson v, Sep 13 2007.
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LINKS
| Eric Weisstein's World of Mathematics, Totative.
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EXAMPLE
| 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. There are 2 of these, so a(15) = 2.
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MATHEMATICA
| fQ[k_, n_] := GCD[k, n] == 1 && GCD[k - 1, n] > 1 && GCD[k + 1, n] > 1; f[n_] := Length@ Select[ Rest[ Range@n - 1], fQ[ #, n] &]; Array[f, 89] (* Robert G. Wilson v *)
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CROSSREFS
| Cf. A132953.
Sequence in context: A096500 A111813 A167156 * A029187 A201863 A035385
Adjacent sequences: A132949 A132950 A132951 * A132953 A132954 A132955
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KEYWORD
| nonn
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AUTHOR
| Leroy Quet, Sep 05 2007
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EXTENSIONS
| Edited and extended by Robert G. Wilson v (rgwv(AT)rgwv.com), Sep 13 2007
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