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A112593
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Triangle where a(1,1) = 1, a(n,m) = number of terms of row (n-1) which are coprime to m. Row n has (2n-1) terms.
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2
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1, 1, 1, 1, 3, 3, 3, 3, 3, 5, 5, 0, 5, 5, 0, 5, 7, 5, 5, 5, 0, 5, 5, 5, 5, 9, 8, 8, 8, 1, 8, 7, 8, 8, 1, 8, 11, 4, 10, 4, 11, 3, 10, 4, 10, 4, 11, 3, 11, 13, 6, 11, 6, 10, 4, 13, 6, 11, 6, 9, 4, 13, 6, 8, 15, 6, 9, 6, 14, 5, 15, 6, 9, 6, 13, 5, 12, 6, 8, 6, 15, 17, 8, 5, 8, 12, 3, 16, 8, 5, 3, 17, 3, 16
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OFFSET
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1,5
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COMMENTS
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GCD(m,0) is considered here to be m, so 0 is coprime to no positive integer but 1.
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LINKS
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EXAMPLE
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Row 5 of the triangle is [7,5,5,5,0,5,5,5,5].
Among these terms there are 9 terms coprime to 1, 8 terms coprime to 2, 8 terms coprime to 3, 8 terms coprime to 4, 1 term coprime to 5, 8 terms coprime to 6, 7 terms coprime to 7, 8 terms coprime to 8, 8 terms coprime to 9, 1 term coprime to 10 and 8 terms coprime to 11. So row 6 is [9,8,8,8,1,8,7,8,8,1,8].
Table begins:
1,
1,1,1,
3,3,3,3,3,
5,5,0,5,5,0,5,
7,5,5,5,0,5,5,5,5,
9,8,8,8,1,8,7,8,8,1,8,
11,4,10,4,11,3,10,4,10,4,11,3,11,
13,6,11,6,10,4,13,6,11,6,9,4,13,6,8,
15,6,9,6,14,5,15,6,9,6,13,5,12,6,8,6,15,
17,8,5,8,12,3,16,8,5,3,17,3,16,8,3,8,17,3,17
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MATHEMATICA
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f[l_] := Append[l, Table[ Count[GCD[Last[l], n], 1], {n, Length[Last[l]] + 2}]]; Flatten[Nest[f, {{1}}, 9]] (* Ray Chandler, Jan 02 2006 *)
t[1, 1] = 1; t[n_, m_] := t[n, m] = Count[ GCD[ Table[ t[n - 1, k], {k, 2n - 3}], m], 1]; Table[ t[n, m], {n, 10}, {m, 2n - 1}] // Flatten (* Robert G. Wilson v *)
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PROG
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(PARI) {print1(s=1, ", "); v=[s]; for(i=2, 10, w=vector(2*i-1); for(j=1, 2*i-1, c=0; for(k=1, 2*i-3, if(gcd(v[k], j)==1, c++)); print1(w[j]=c, ", ")); v=w)} (Brockhaus)
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CROSSREFS
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KEYWORD
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nonn,tabf
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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