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
Examples
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
Links
- Ivan Neretin, Rows n = 1..101, flattened
Crossrefs
Row sums are in A114718. - Klaus Brockhaus, Jun 01 2009
Programs
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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 *)
Extensions
Extended by Ray Chandler, Dec 24 2005
Comments