%I
%S 1,1,0,1,2,0,1,0,3,0,1,2,3,4,0,1,0,0,0,5,0,1,2,3,4,5,6,0,1,0,3,0,5,0,
%T 7,0,1,2,0,4,5,0,7,8,0,1,0,3,0,0,0,7,0,9,0,1,2,3,4,5,6,7,8,9,10,0,1,0,
%U 0,0,5,0,7,0,0,0,11,0,1,2,3,4,5,6,7,8,9,10,11,12,0
%N Relative prime triangle, read by rows.
%C Row sums = A023896, (reduced residue system mod n): (1, 1, 3, 4, 10, 6, 21,...). [From _Gary W. Adamson_, Aug 27 2008]
%F T(n,k) = k if a relative prime of n; 0 otherwise. Replace the "1's" of A054521 with their corresponding column numbers; leaving the zeros.
%F Equals A054521 * A127648 as infinite lower triangular matrices. [From _Gary W. Adamson_, Aug 27 2008]
%e Row 4 = (1, 0, 3, 0) since 1 and 3 are relative primes of 4.
%e First few rows of the triangle are:
%e 1;
%e 1, 0;
%e 1, 2, 0;
%e 1, 0, 3, 0;
%e 1, 2, 3, 4, 0;
%e 1, 0, 0, 0, 5, 0;
%e 1, 2, 3, 4, 5, 6, 0;
%e ...
%o (PARI) [Contribution from _M. F. Hasler_, Mar 02 2012] (Start)
%o T127368(n,k)={gcd(n,k)==1 & return(k)}
%o A127368(n)=T127368( t=(sqrt(8*n)+1)\2, nbinomial(t, 2)) \\ (End)
%Y Cf. A054521.
%Y A054521, A023896 [From _Gary W. Adamson_, Aug 27 2008]
%K nonn,tabl
%O 1,5
%A _Gary W. Adamson_, Jan 11 2007
%E Corrected at the suggestion of Kevin Ryde by _Alois P. Heinz_, Mar 02 2012
