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a(n) = A306912(n) - 2.
0

%I #27 Dec 20 2024 13:03:30

%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 a(n) = A306912(n) - 2.

%C 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 a(n) = Sum_{k=2..n} A000837(k).

%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}]

%Y Cf. A000837, A306912.

%K nonn

%O 1,3

%A _Clark Kimberling_, Mar 09 2012

%E New name and edits made by _Clark Kimberling_, Dec 18 2024