A229219 a(n) = maximal length of partitions of prime(n) into distinct primes.

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, 9, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 12, 11, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 14, 13, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14

Offset: 1

Author

Arkadiusz Wesolowski, Nov 10 2013

Keywords

• nonn
• changed

Examples

			a(11) = 4 because prime(11) = 31 = 2 + 3 + 7 + 19, but 31 is not a sum of 5 or more distinct primes.
		

Links

• David A. Corneth, Table of n, a(n) for n = 1..10000
• G. L. Honaker, Jr. and Chris Caldwell, Prime Curios! 11
• Wikipedia, Knapsack problem

Crossrefs

Cf. A000040, A070215.

Programs

Mathematica

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 *)