This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A209489 #27 Dec 20 2024 13:03:30
%S A209489 0,1,3,6,12,19,33,50,77,111,166,229,329,448,615,824,1120,1467,1956,
%T A209489 2538,3313,4258,5512,6993,8944,11278,14258,17838,22402,27788,34629,
%U A209489 42747,52832,64844,79706,97232,118868,144392,175474,212168,256750
%N A209489 a(n) = A306912(n) - 2.
%C A209489 Former name was "Number of partitions of 1 into rational parts a/b satisfying 0<a<b<=n", but that was wrong, that is A269926, a different sequence. - _N. J. A. Sloane_, Dec 20 2024
%F A209489 a(n) = Sum_{k=2..n} A000837(k).
%t A209489 p[n_] := p[n] = IntegerPartitions[n];
%t A209489 l[n_] := Length[p[n]];
%t A209489 p[n_, j_] := p[n, j] = Part[p[n], j]
%t A209489 g[n_, j_] := g[n, j] = Apply[GCD, p[n, j]]
%t A209489 h[n_] := h[n] = Table[g[n, j], {j, 1, l[n]}]
%t A209489 c[n_] := c[n] = Count[h[n], 1]
%t A209489 Table[c[n], {n, 0, 45}] (* A000837 *)
%t A209489 s[n_] := Sum[c[k], {k, 1, n}]
%t A209489 Table[s[n] - 1, {n, 1, 45}]
%Y A209489 Cf. A000837, A306912.
%K A209489 nonn
%O A209489 1,3
%A A209489 _Clark Kimberling_, Mar 09 2012
%E A209489 New name and edits made by _Clark Kimberling_, Dec 18 2024