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 A168173 #7 May 11 2019 16:57:08
%S A168173 0,1,1,1,2,3,3,4,4,6,8,12,13,16,18,21,25,32,38,46,55,65,78,92,103,122,
%T A168173 140,165,193,229,264,305,345,395,451,517,590,682,781,893,1013,1165,
%U A168173 1324,1518,1717,1945,2188,2468,2753,3089,3457,3865,4321,4856,5441,6108,6831
%N A168173 Number of partitions of n in which the sum of reciprocals of parts is less than 1.
%p A168173 a := proc (n) local P, ct, j: with(combinat): P := partition(n): ct := 0: for j to numbpart(n) do if add(1/P[j][i], i = 1 .. nops(P[j])) < 1 then ct := ct+1 else end if end do: ct end proc: seq(a(n), n = 1 .. 60); # _Emeric Deutsch_, Dec 02 2009
%t A168173 Table[Count[IntegerPartitions[n],_?(Total[1/#]<1&)],{n,60}] (* _Harvey P. Dale_, Dec 14 2012 *)
%Y A168173 Cf. A051908.
%K A168173 nonn
%O A168173 1,5
%A A168173 _Vladeta Jovovic_, Nov 19 2009
%E A168173 Extended by _Emeric Deutsch_, Dec 02 2009