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

%I A212607 #23 May 13 2019 11:19:58
%S A212607 1,2,3,5,8,14,21,38,70,129,238,440,504,949,1790,2301,4363,8272,12408,
%T A212607 23604,26675,45724,87781,168549,181989,351076,677339,1306894,1399054,
%U A212607 2709128,2795144,5423805,10525050
%N A212607 Number of distinct sums <= 1 of distinct reciprocals of integers <= n.
%e A212607 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 A212607 s:= proc(n) option remember;
%p A212607       `if`(n=0, {0}, map(x-> `if`(n-1<n*x, x, [x, x+1/n][]), s(n-1)))
%p A212607     end:
%p A212607 a:= n-> nops(s(n)):
%p A212607 seq(a(n), n=0..20);  # _Alois P. Heinz_, May 23 2012
%t A212607 s[_] := s[n] = If[n == 0, {0}, If[n-1 < n*#, #, {#, # + 1/n}]& /@ s[n-1] // Flatten];
%t A212607 a[n_] := Length[s[n]];
%t A212607 Table[Print[n, " ", a[n]]; a[n], {n, 0, 32}] (* _Jean-François Alcover_, May 13 2019, after _Alois P. Heinz_ *)
%Y A212607 For possibly non-distinct reciprocals, see A212606.
%Y A212607 Cf. A020473, A092669, A092671, A208480.
%K A212607 nonn
%O A212607 0,2
%A A212607 _Max Alekseyev_, May 22 2012
%E A212607 a(27)-a(32) from _Alois P. Heinz_, May 23 2012