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

%I A112592 #14 Mar 11 2014 01:32:16
%S A112592 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,
%T A112592 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,
%U A112592 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
%N A112592 Triangle where a(1,1) = 0, a(n,m) = number of terms of row (n-1) which are coprime to m.
%C A112592 GCD(m,0) is considered here to be m, so 0 is coprime to no positive integer but 1.
%H A112592 Diana Mecum, <a href="/A112592/b112592.txt">Table of n, a(n) for n = 1..2000</a> [From _Diana L. Mecum_, Aug 12 2008]
%e A112592 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].
%e A112592 0,
%e A112592 1,0,
%e A112592 2,1,1,
%e A112592 3,2,3,2,
%e A112592 4,2,2,2,4,
%e A112592 5,0,5,0,5,0,
%e A112592 6,3,3,3,0,3,3,
%e A112592 7,5,0,5,6,0,6,5,
%e A112592 8,4,4,4,3,4,5,4,4
%t A112592 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_ *)
%Y A112592 Cf. A112599.
%Y A112592 Row sums are in A114719. [From _Klaus Brockhaus_, Jun 01 2009]
%K A112592 nonn,tabl
%O A112592 1,4
%A A112592 _Leroy Quet_, Dec 24 2005
%E A112592 More terms from _Robert G. Wilson v_, Dec 27 2005
%E A112592 Terms a(100) through a(2000) from _Diana L. Mecum_, Aug 12 2008