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%I #5 Mar 30 2012 18:58:15
%S 0,1,3,6,12,19,33,50,77,111,166,229,329,448,615,824,1120,1467,1956,
%T 2538,3313,4258,5512,6993,8944,11278,14258,17838,22402,27788,34629,
%U 42747,52832,64844,79706,97232,118868,144392,175474,212168,256750
%N Number of partitions of 1 into rational parts a/b satisfying 0<a<b<=n.
%F a(n)=a(n-1)-1+(number of partitions of n into relatively prime parts).
%e a(1)=0.
%e a(2)=1 counts 1/2 + 1/2.
%e a(3)=3 counts 1/2 + 1/2, 1/3 + 1/3 + 1/3, and 1/3 + 2/3.
%t p[n_] := p[n] = IntegerPartitions[n];
%t l[n_] := Length[p[n]];
%t p[n_, j_] := p[n, j] = Part[p[n], j]
%t g[n_, j_] := g[n, j] = Apply[GCD, p[n, j]]
%t h[n_] := h[n] = Table[g[n, j], {j, 1, l[n]}]
%t c[n_] := c[n] = Count[h[n], 1]
%t Table[c[n], {n, 0, 45}] (* A000837 *)
%t s[n_] := Sum[c[k], {k, 1, n}]
%t Table[s[n] - 1, {n, 1, 45}] (* A209489 *)
%Y Cf. A000837.
%K nonn
%O 1,3
%A _Clark Kimberling_, Mar 09 2012
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