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%I #42 Mar 02 2016 04:40:32
%S 1,2,3,3,4,4,5,5,5,5,6,6,6,6,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,9,9,9,9,9,
%T 9,9,9,9,9,9,9,10,10,10,10,10,10,10,10,10,10,10,10,10,10,11,11,11,11,
%U 11,11,11,11,11,11,11,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12
%N Greatest number k such that p(k) <= n, p(k) being the number of unrestricted partitions of k.
%C Sort of "InversePartitionsP".
%t a[n_] := For[k=1, True, k++, If[PartitionsP[k]>n, Return[k-1]]]; Table[ a[n], {n, 100}]
%o (PARI) a(n)=my(k=1);while(numbpart(k)<=n,k++); k-1 \\ _Charles R Greathouse IV_, Jan 14 2013
%Y Cf. A000041.
%K nonn
%O 1,2
%A _Jean-François Alcover_, Jan 14 2013
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