

A132952


a(n) is the number of isolated totatives of n.


4



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
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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 (k1) nor (k+1) are coprime to n.
a(2n) = phi(2n), where phi(n) = A000010(n).
If k is an isolated totative so is nk.  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

Antti Karttunen, Table of n, a(n) for n = 1..16384
Eric Weisstein's World of Mathematics, Totative.
Antti Karttunen, Data supplement: n, a(n) computed for n = 1..65537


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 *)


PROG

(PARI) A132952(n) = { my(s=0, pg=0, g=1, ng); for(k=1, n1, if((1!=(ng=gcd(n, k+1)))&&(1==g)&&(1!=pg), s++); pg = g; g = ng); (s); }; \\ Antti Karttunen, Nov 01 2018


CROSSREFS

Cf. A132953.
Sequence in context: A282849 A111813 A167156 * A319998 A336120 A029187
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



