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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. 3

%I

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

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

%H Diana Mecum, <a href="/A112592/b112592.txt">Table of n, a(n) for n = 1..2000</a> [From Diana Mecum (diana.mecum(AT)gmail.com), Aug 12 2008]

%e 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 0,

%e 1,0,

%e 2,1,1,

%e 3,2,3,2,

%e 4,2,2,2,4,

%e 5,0,5,0,5,0,

%e 6,3,3,3,0,3,3,

%e 7,5,0,5,6,0,6,5,

%e 8,4,4,4,3,4,5,4,4

%t 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 Cf. A112599.

%Y Row sums are in A114719. [From _Klaus Brockhaus_, Jun 01 2009]

%K nonn,tabl

%O 1,4

%A Leroy Quet, Dec 24 2005

%E More terms from _Robert G. Wilson v_, Dec 27 2005

%E Terms a(100) through a(2000) from Diana Mecum (diana.mecum(AT)gmail.com), Aug 12 2008

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