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Search: id:A132952
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| A132952 |
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a(n) = number of isolated totatives of n. |
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+0
2
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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; listen)
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OFFSET
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1,4
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COMMENT
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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
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Eric Weisstein's World of Mathematics, Totative.
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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. There are 2 of these, so a(15) = 2.
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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_] := Length@ Select[ Rest[ Range@n - 1], fQ[ #, n] &]; Array[f, 89] (* Robert G. Wilson v *)
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CROSSREFS
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Cf. A132953.
Sequence in context: A112631 A096500 A111813 this_sequence A029187 A035385 A051629
Adjacent sequences: A132949 A132950 A132951 this_sequence A132953 A132954 A132955
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KEYWORD
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nonn
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AUTHOR
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Leroy Quet (qq-quet(AT)mindspring.com), Sep 05 2007
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EXTENSIONS
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Edited and extended by Robert G. Wilson v (rgwv(AT)rgwv.com), Sep 13 2007
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