A112599 Triangle where a(1,1) = 1, a(n,m) = number of terms of row (n-1) which are coprime to m.

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

Offset

1,4

Comments

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

Links

Ivan Neretin, Rows n = 1..101, flattened

Example

Row 6 of the triangle is [5,0,4,0,4,0]. Among these terms there are 6 terms coprime to 1, 1 term coprime to 2, 3 terms coprime to 3, 1 term coprime to 4, 2 terms coprime to 5, 1 term coprime to 6 and 3 terms coprime to 7. So row 7 is [6,1,3,1,2,1,3].
1
1 1
2 2 2
3 0 3 0
4 2 0 2 2
5 0 4 0 4 0
6 1 3 1 2 1 3
7 5 4 5 7 3 7 5
8 7 7 7 5 6 5 7 7
9 7 8 7 7 7 4 7 8 5

Mathematica

f[l_] := Block[{p, t}, p = l[[ -1]]; k = Length[p]; t = Table[ Sum[ If[GCD[p[[j]], n] == 1, 1, 0], {j, k}], {n, k + 1}]; Return[Append[l, t]]; ]; Flatten[Nest[f, {{1}}, 13]] (* Ray Chandler, Dec 24 2005 *)

Crossrefs

Row sums are in A114718. - Klaus Brockhaus, Jun 01 2009

Sequence in context: A307296 A004489 A305384 * A347905 A308119 A307299

Adjacent sequences: A112596 A112597 A112598 * A112600 A112601 A112602

Keyword

nonn,tabl,look

Author

Leroy Quet, Dec 21 2005

Extensions

Extended by Ray Chandler, Dec 24 2005

Status

approved