A212607 Number of distinct sums <= 1 of distinct reciprocals of integers <= n.

1, 2, 3, 5, 8, 14, 21, 38, 70, 129, 238, 440, 504, 949, 1790, 2301, 4363, 8272, 12408, 23604, 26675, 45724, 87781, 168549, 181989, 351076, 677339, 1306894, 1399054, 2709128, 2795144, 5423805, 10525050

Offset: 0

Author

Max Alekseyev, May 22 2012

Keywords

• nonn

Examples

			a(3) = 5 counts numbers { 0, 1/3, 1/2, 5/6, 1 }, each of which is can be represented as the sum of distinct reciprocals 1/1, 1/2, and 1/3.
		

Crossrefs

For possibly non-distinct reciprocals, see A212606.

Cf. A020473, A092669, A092671, A208480.

Programs

Maple

s:= proc(n) option remember;
      `if`(n=0, {0}, map(x-> `if`(n-1 nops(s(n)):
seq(a(n), n=0..20);  # Alois P. Heinz, May 23 2012

Mathematica

s[_] := s[n] = If[n == 0, {0}, If[n-1 < n*#, #, {#, # + 1/n}]& /@ s[n-1] // Flatten];
a[n_] := Length[s[n]];
Table[Print[n, " ", a[n]]; a[n], {n, 0, 32}] (* Jean-François Alcover, May 13 2019, after Alois P. Heinz *)

Extensions

a(27)-a(32) from Alois P. Heinz, May 23 2012