%I #12 Apr 03 2023 10:36:13
%S 1,1,2,2,1,2,4,3,4,4,4,4,6,5,6,6,6,6,6,6,6,7,8,8,8,8,8,8,8,8,9,10,10,
%T 9,10,10,10,10,10,10,10,10,10,10,12,11,12,12,12,12,12,12,12,12,12,12,
%U 12,12,12,14,13,14,14,14,14,14,14,14,14,14,14,14,14,14
%N a(n) = maximal length of partitions of prime(n) into distinct primes.
%H G. L. Honaker, Jr. and Chris Caldwell, <a href="https://t5k.org/curios/cpage/12048.html">Prime Curios! 11</a>
%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Knapsack_problem">Knapsack problem</a>
%e a(11) = 4 because prime(11) = 31 = 2 + 3 + 7 + 19, but 31 is not a sum of 5 or more distinct primes.
%t nn = 20; p = Prime[Range[nn]]; s = Subsets[p]; t2 = Table[Select[s, Total[#] == n &], {n, p}]; Table[Max[Length /@ t2[[n]]], {n, nn}] (* _T. D. Noe_, Nov 13 2013 *)
%Y Cf. A000040, A070215.
%K nonn
%O 1,3
%A _Arkadiusz Wesolowski_, Nov 10 2013