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

Author

Leroy Quet, Dec 24 2005

Keywords

• nonn
• tabl

Comments

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

Examples

			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
		

Links

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

Crossrefs

Cf. A112599.

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

Programs

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 *)

Extensions

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

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