A024936 a(n) = maximal length of partitions of n into distinct primes or -1 if there is no such partition.

0, -1, 1, 1, -1, 2, -1, 2, 2, 2, 3, 1, 3, 2, 3, 3, 3, 4, 3, 3, 3, 4, 3, 4, 3, 4, 4, 4, 5, 4, 5, 4, 4, 4, 5, 4, 5, 4, 5, 5, 5, 6, 5, 5, 5, 6, 5, 6, 5, 6, 5, 6, 5, 6, 5, 6, 6, 6, 7, 6, 7, 6, 6, 6, 7, 6, 7, 6, 7, 6, 7, 6, 7, 6, 7, 7, 7, 8, 7, 7, 7, 8, 7, 8, 7, 7, 7, 8, 7, 8, 7, 8, 7, 8, 7, 8, 7, 8, 8, 8, 9, 8, 7, 8, 8, 8, 9, 8, 9, 8, 9, 8

Offset: 0

Author

Clark Kimberling

Keywords

• sign

Examples

			a(12) = 3 because 12 = 2+3+7, but 12 is not a sum of 4 or more distinct primes.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..2000

Crossrefs

a(n) + 1 = row length of A219180(n).

Programs

Mathematica

ReplaceAll[Table[Max[Length /@ Select[IntegerPartitions[n, n, Prime[Range[n]]],  DuplicateFreeQ[#] &]], {n, 0, 100}] /. -Infinity -> -1] (* Robert Price, Apr 23 2025 *)

Extensions

More terms from Naohiro Nomoto, Oct 28 2001

More terms from David Wasserman, Jan 23 2003

Offset changed and edited by Alois P. Heinz, Nov 13 2012