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A133755 Number of positive integers less than n/3 that are coprime to n. 1
0, 0, 0, 1, 1, 1, 2, 1, 2, 2, 3, 1, 4, 2, 3, 3, 5, 2, 6, 2, 4, 4, 7, 3, 7, 4, 6, 4, 9, 2, 10, 5, 7, 6, 8, 4, 12, 6, 8, 6, 13, 4, 14, 6, 8, 8, 15, 5, 14, 6, 11, 8, 17, 6, 14, 8, 12, 10, 19, 6, 20, 10, 12, 11, 16, 6, 22, 10, 15, 8, 23, 8, 24, 12, 13, 12, 20, 8, 26, 10, 18, 14, 27, 8, 22, 14, 19, 14 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,7

COMMENTS

If the definition were changed to "... <= ...", the term a(3) would change from 0 to 1, but all others remain the same. Obviously a(n) is also the number of reduced fractions < 1/3 with denominator equal to n.

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..10000

FORMULA

a(n) = Sum_{d|n} mu(d)*[n/(3d)] = Sum_{d|n} mu(n/d)*d/3. - Max Alekseyev

For n>3, a(n) = (eulerphi(n) + c) / 3 where the term c is nonzero if and only if eulerphi(n) is not divisible by 3. In the latter case n=3^t*p1^k1*...*pm^km where every prime pi=2 (mod 3) and t=0 or 1 and the value of c is given by: c = (-1)^(t+k1+...+km) * 2^(m-1). - Max Alekseyev, Jan 07 2007

MATHEMATICA

f[n_] := Block[{c = 0, k = 1, lmt = n/3}, While[k < lmt, If[ GCD[k, n] == 1, c++ ]; k++ ]; c]; Array[f, 88] (* Robert G. Wilson v, Jan 06 2008 *)

PROG

(PARI) vector(100, i, sum(j=1, (i-1)\3, gcd(i, j)==1))

(PARI) a(n)=sumdiv(n, d, moebius(n\d)*(d\3)) /* Max Alekseyev */

(PARI) { a(n) = ( eulerphi(n) + if(eulerphi(n)%3, (-1)^bigomega(n)*2^(omega(n)-1-(n%3==0))) )/3 } /* Max Alekseyev */

CROSSREFS

Sequence in context: A071287 A072084 A336471 * A336470 A070104 A131085

Adjacent sequences:  A133752 A133753 A133754 * A133756 A133757 A133758

KEYWORD

nonn

AUTHOR

M. F. Hasler, Jan 04 2008, Jan 08 2008

STATUS

approved

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Last modified August 13 06:22 EDT 2020. Contains 336442 sequences. (Running on oeis4.)