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A132952 a(n) = number of isolated totatives of n. 1
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; text; internal format)
OFFSET

1,4

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.

LINKS

Table of n, a(n) for n=1..89.

Eric Weisstein's World of Mathematics, Totative.

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.

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 *)

CROSSREFS

Cf. A132953.

Sequence in context: A231563 A111813 A167156 * A029187 A201863 A035385

Adjacent sequences:  A132949 A132950 A132951 * A132953 A132954 A132955

KEYWORD

nonn

AUTHOR

Leroy Quet, Sep 05 2007

EXTENSIONS

Edited and extended by Robert G. Wilson v, Sep 13 2007

STATUS

approved

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Last modified October 24 23:00 EDT 2014. Contains 248516 sequences.