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

%I A112599 #18 Oct 11 2019 16:38:26
%S A112599 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,
%T A112599 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,
%U A112599 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
%N A112599 Triangle where a(1,1) = 1, a(n,m) = number of terms of row (n-1) which are coprime to m.
%C A112599 GCD(m,0) is considered here to be m, so 0 is coprime to no positive integer but 1.
%H A112599 Ivan Neretin, <a href="/A112599/b112599.txt">Rows n = 1..101, flattened</a>
%e A112599 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].
%e A112599 1
%e A112599 1 1
%e A112599 2 2 2
%e A112599 3 0 3 0
%e A112599 4 2 0 2 2
%e A112599 5 0 4 0 4 0
%e A112599 6 1 3 1 2 1 3
%e A112599 7 5 4 5 7 3 7 5
%e A112599 8 7 7 7 5 6 5 7 7
%e A112599 9 7 8 7 7 7 4 7 8 5
%t A112599 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 *)
%Y A112599 Row sums are in A114718. - _Klaus Brockhaus_, Jun 01 2009
%K A112599 nonn,tabl,look
%O A112599 1,4
%A A112599 _Leroy Quet_, Dec 21 2005
%E A112599 Extended by _Ray Chandler_, Dec 24 2005