%I #9 Mar 01 2014 19:41:29
%S 2,4,5,6,7,8,8,9,9,10,10,11,11,11,12,12,12,13,13,13,13,14,14,14,14,14,
%T 15,15,15,15,15,16,16,16,16,16,16,17,17,17,17,17,17,17,17,18,18,18,18,
%U 18,18,18,18,19,19,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,20,20,20,20,21,21,21,21,21,21,21,21,21,21,21,21,21,22,22,22,22,22,22,22,22,22,22,22,22
%N Greatest number k such that A000009(k) <= n.
%C Inverse of A000009, the sequence of "restricted" partitions (partitions of integers into distinct parts).
%H Jean-François Alcover, <a href="/A238461/b238461.txt">Table of n, a(n) for n = 1..1000</a>
%e q(12) = 15, therefore a(15) = 12.
%t a[n_] := For[k = 1, True, k++, If[PartitionsQ[k] > n, Return[k-1]]]; Table[a[n], {n, 100}]
%Y Cf. A000009, A000041, A198194.
%K nonn
%O 1,1
%A _Jean-François Alcover_, Feb 27 2014