A112592 Triangle where a(1,1) = 0, a(n,m) = number of terms of row (n-1) which are coprime to m.

0, 1, 0, 2, 1, 1, 3, 2, 3, 2, 4, 2, 2, 2, 4, 5, 0, 5, 0, 5, 0, 6, 3, 3, 3, 0, 3, 3, 7, 5, 0, 5, 6, 0, 6, 5, 8, 4, 4, 4, 3, 4, 5, 4, 4, 9, 2, 8, 2, 8, 1, 9, 2, 8, 1, 10, 4, 8, 4, 10, 2, 10, 4, 8, 4, 10, 11, 0, 11, 0, 7, 0, 11, 0, 11, 0, 11, 0, 12, 6, 6, 6, 6, 6, 5, 6, 6, 6, 1, 6, 6, 13, 2, 2, 2, 12, 2, 13, 2

Offset

1,4

Comments

GCD(m,0) is considered here to be m, so 0 is coprime to no positive integer but 1.

Links

Diana Mecum, Table of n, a(n) for n = 1..2000 [From Diana L. Mecum, Aug 12 2008]

Example

Row 6 of the triangle is [5,0,5,0,5,0]. Among these terms there are 6 terms coprime to 1, 3 terms coprime to 2, 3 terms coprime to 3, 3 terms coprime to 4, 0 terms coprime to 5, 3 terms coprime to 6 and 3 terms coprime to 7. So row 7 is [6,3,3,3,0,3,3].
0,
1,0,
2,1,1,
3,2,3,2,
4,2,2,2,4,
5,0,5,0,5,0,
6,3,3,3,0,3,3,
7,5,0,5,6,0,6,5,
8,4,4,4,3,4,5,4,4

Mathematica

f[l_] := Block[{p, t}, p = l[[ -1]]; k = Length@p; t = Table[Count[GCD[p, n], 1], {n, k + 1}]; Return@Append[l, t]; ]; Nest[f, {{0}}, 13] // Flatten (* Robert G. Wilson v *)

Crossrefs

Cf. A112599.

Row sums are in A114719. [From Klaus Brockhaus, Jun 01 2009]

Sequence in context: A060117 A196526 A234504 * A370666 A351466 A070036

Adjacent sequences: A112589 A112590 A112591 * A112593 A112594 A112595

Keyword

nonn,tabl

Author

Leroy Quet, Dec 24 2005

Extensions

More terms from Robert G. Wilson v, Dec 27 2005

Terms a(100) through a(2000) from Diana L. Mecum, Aug 12 2008

Status

approved