OFFSET
1,5
COMMENTS
GCD(m,0) is considered here to be m, so 0 is coprime to no positive integer but 1.
EXAMPLE
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
MATHEMATICA
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 *)
PROG
(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)
CROSSREFS
KEYWORD
nonn,tabf
AUTHOR
Leroy Quet, Dec 24 2005
EXTENSIONS
STATUS
approved