A071335 Number of partitions of n into sum of at most three primes.

0, 1, 1, 1, 2, 2, 3, 2, 3, 3, 3, 3, 4, 3, 4, 4, 5, 4, 5, 4, 6, 5, 6, 6, 6, 6, 7, 5, 8, 5, 8, 5, 10, 6, 8, 8, 10, 6, 11, 5, 12, 7, 12, 7, 13, 7, 14, 9, 13, 9, 15, 7, 17, 8, 15, 8, 17, 7, 17, 10, 18, 9, 20, 8, 21, 11, 21, 8, 21, 7, 23, 11, 23, 11, 23, 10, 28, 12, 25, 11, 26

Offset: 1

Author

Reinhard Zumkeller, May 19 2002

Keywords

• nonn
• look

Comments

a(n) = A010051(n) + A061358(n) + A068307(n). [From Reinhard Zumkeller, Aug 08 2009]

Examples

			a(21)=6 as 21 = 2+19 = 2+2+17 = 3+5+13 = 3+7+11 = 5+5+11 = 7+7+7.
		

Links

• T. D. Noe, Table of n, a(n) for n=1..10000

Crossrefs

Cf. A002375, A068307, A025583.

Programs

Mathematica

goldbachcount[p1_] := (parts=IntegerPartitions[p1, 3]; count=0; n=1;
  While[n<=Length[parts], If[Intersection[Flatten[PrimeQ[parts[[n]]]]][[1]]==True, count++]; n++]; count); Table[goldbachcount[i], {i, 1, 100}] (* Frank M Jackson, Mar 25 2013 *)
Table[Length[Select[IntegerPartitions[n,3],AllTrue[#,PrimeQ]&]],{n,90}] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Oct 21 2016 *)