A212607 - OEIS

%I #23 May 13 2019 11:19:58

%S 1,2,3,5,8,14,21,38,70,129,238,440,504,949,1790,2301,4363,8272,12408,

%T 23604,26675,45724,87781,168549,181989,351076,677339,1306894,1399054,

%U 2709128,2795144,5423805,10525050

%N Number of distinct sums <= 1 of distinct reciprocals of integers <= n.

%e 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.

%p s:= proc(n) option remember;

%p       `if`(n=0, {0}, map(x-> `if`(n-1<n*x, x, [x, x+1/n][]), s(n-1)))

%p     end:

%p a:= n-> nops(s(n)):

%p seq(a(n), n=0..20);  # _Alois P. Heinz_, May 23 2012

%t s[_] := s[n] = If[n == 0, {0}, If[n-1 < n*#, #, {#, # + 1/n}]& /@ s[n-1] // Flatten];

%t a[n_] := Length[s[n]];

%t Table[Print[n, " ", a[n]]; a[n], {n, 0, 32}] (* _Jean-François Alcover_, May 13 2019, after _Alois P. Heinz_ *)

%Y For possibly non-distinct reciprocals, see A212606.

%Y Cf. A020473, A092669, A092671, A208480.

%K nonn

%O 0,2

%A _Max Alekseyev_, May 22 2012

%E a(27)-a(32) from _Alois P. Heinz_, May 23 2012