A097560 a(n) = number of terms among {a(1), a(2), a(3), ..., a(n-1)} that are coprime to n; a(1)=3.

3, 1, 1, 3, 4, 2, 6, 4, 5, 4, 10, 3, 12, 6, 6, 6, 16, 3, 18, 6, 9, 8, 22, 3, 22, 9, 12, 10, 28, 2, 30, 10, 14, 10, 26, 3, 36, 11, 19, 12, 40, 5, 42, 13, 17, 16, 46, 8, 45, 14, 28, 16, 52, 8, 42, 17, 33, 19, 58, 8, 60, 20, 34, 20, 49, 10, 66, 19, 42, 18, 70, 12, 72, 22, 34, 19, 61, 13, 78

Offset

1,1

Comments

A family of related sequences can be generated using different positive integers for a(1). a(1)=1 gives sequence A096216.

Links

Table of n, a(n) for n=1..79.

Example

a(8)=4 because among the first seven terms, namely 3,1,1,3,4,2,6, there are 4 terms that are relatively prime to 8 (3,1,1 and 3).

Maple

a[1]:=3: for n from 2 to 100 do s:=0: for j from 1 to n-1 do if gcd(a[j], n)=1 then s:=s+1 else s:=s fi od: a[n]:=s: od: seq(a[n], n=1..84); # Emeric Deutsch, Aug 03 2005

Mathematica

a[1] = 3; a[n_] := a[n] = Count[ GCD[ Table[ a[i], {i, n - 1}], n], 1]; Array[a, 79] (* Robert G. Wilson v, Dec 27 2005 *)

Crossrefs

Cf. A096216.

Sequence in context: A035690 A124794 A206496 * A218905 A027960 A319182

Adjacent sequences: A097557 A097558 A097559 * A097561 A097562 A097563

Keyword

nonn

Author

Leroy Quet, Aug 27 2004

Extensions

More terms from John W. Layman, Sep 27 2004

Status

approved