1,5

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

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

f[l_] := Append[l, Table[ Count[GCD[Last[l], n], 1], {n, Length[Last[l]] + 2}]]; Flatten[Nest[f, {{1}}, 9]] (*Chandler*)

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 *)

(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)

Cf. A112599.

Adjacent sequences: A112590 A112591 A112592 this_sequence A112594 A112595 A112596

Sequence in context: A105159 A050499 A114227 this_sequence A113215 A105591 A130497

nonn,tabf

Leroy Quet (qq-quet(AT)mindspring.com), Dec 24 2005

More terms from Robert G. Wilson v (rgwv(at)rgwv.com), Klaus Brockhaus (klaus-brockhaus(AT)t-online.de) and Ray Chandler (rayjchandler(AT)sbcglobal.net), Jan 02 2006