A112620 If b(n,1) = n; b(n,m) is number of terms among {b(n,1), b(n,2), ..., b(n,m-1)} which are coprime to m, then a(n) = b(n,n).

1, 0, 1, 1, 3, 1, 5, 4, 5, 3, 9, 3, 11, 8, 6, 9, 15, 5, 17, 8, 12, 11, 21, 7, 18, 13, 12, 12, 27, 7, 29, 19, 15, 18, 24, 12, 35, 23, 23, 17, 39, 12, 41, 20, 19, 25, 45, 18, 38, 24, 23, 26, 51, 21, 40, 30, 35, 31, 57, 18, 59, 38, 37, 38, 47, 24, 65, 36, 38, 27, 69, 24, 71, 41, 36, 43

Offset

1,5

Comments

When calculating the sequence, GCD(0,m) = m, so 0 is to be considered coprime only to 1.

Links

Table of n, a(n) for n=1..76.

Example

Array b(n,m) (of which this sequence in the main diagonal) begins like this:
1,1,2,2,4,2,6,2,7,... (sequence A096216)
2,0,1,1,3,2,5,4,6,... (sequence A097559)
3,1,1,3,4,2,6,4,5,... (sequence A097560)
4,0,1,1,3,2,5,4,6,... (sequence A097559 except for first term)
5,1,2,2,3,2,6,3,5,... (sequence A097562)
6,0,0,0,1,1,3,3,2,... (sequence A097606)

Mathematica

b[n_] := Module[{a}, a[1] = n; a[k_] := a[k] = Count[ GCD[ Table[ a[i], {i, k - 1}], k], 1]; a[n]]; Array[b, 76] (* Robert G. Wilson v, Dec 27 2005 *)

Crossrefs

Cf. A096216, A097559, A097560, A097562, A097606.

Sequence in context: A011090 A260629 A339919 * A325766 A021321 A129676

Adjacent sequences: A112617 A112618 A112619 * A112621 A112622 A112623

Keyword

nonn

Author

Leroy Quet, Dec 25 2005

Extensions

a(17)-a(76) from Robert G. Wilson v, Dec 27 2005

Status

approved