%I
%S 1,2,1,3,1,1,4,3,2,1,5,2,1,1,1,6,5,4,3,2,1,7,3,5,1,3,1,1,8,7,2,5,4,1,
%T 2,1,9,4,7,3,1,2,3,1,1,10,9,8,7,6,5,4,3,2,1,11,5,3,2,7,1,5,1,1,1,1,12,
%U 11,10,9,8,7,6,5,4,3,2,1,13,6,11,5,9,4,1,3,5,2,3,1,1,14,13,4,11,2,3,8,7,2
%N Numerators of fractions n/m in array by antidiagonals.
%C Column m has period m.  _Clark Kimberling_, Jul 04 2013
%C Read as a triangle with antidiagonals for rows, T(n,k) gives the number of distinct locations at which two points the same distance from a center rotating around that center in the same direction at speeds n+1 and k will coincide.  _Thomas Anton_, Nov 23 2018
%H Clark Kimberling, <a href="/A112543/b112543.txt">Antidiagonals n = 1..60, flattened</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/ExponentialIntegral.html">Exponential Integral</a>
%F For n/m: g.f.: x/(1x)*log(1/(1y)), e.g.f.: x*e^x*(Ei(y)log(y)+gamma) = x*e^x*integral_t=0^y (e^t1)dt.
%F n/gcd(m,n).  _Clark Kimberling_, Jul 04 2013
%e a(2,4)=1/2 because 2/4 = 1/2.
%e Northwest corner:
%e 1 2 3 4 5 6 7
%e 1 1 3 2 5 3 7
%e 1 2 1 4 5 2 7
%e 1 1 3 1 5 3 7
%e 1 2 3 4 1 1 7
%e 1 1 1 2 5 1 7
%e 1 2 3 4 5 6 1
%t d[m_, n_] := n/GCD[m, n]; z = 12;
%t TableForm[Table[d[m, n], {m, 1, z}, {n, 1, z}] ] (*array*)
%t Flatten[Table[d[k, m + 1  k], {m, 1, z}, {k, 1, m}]] (*sequence*)
%t (* _Clark Kimberling_, Jul 04 2013 *)
%o (PARI) t1(n)=binomial(floor(3/2+sqrt(2*n)),2)n+1 t2(n)=nbinomial(floor(1/2+sqrt(2*n)),2) vector(100,n,t1(n)/gcd(t1(n),t2(n)))
%Y Denominators in A112544. Reduced version of A004736/A002260.
%K easy,frac,nonn,tabl
%O 1,2
%A _Franklin T. AdamsWatters_, Sep 11 2005
%E Keyword tabl added by _Franklin T. AdamsWatters_, Sep 02 2009
