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

1,5

Comments

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

Links

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

Example

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

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 *)

Crossrefs

Cf. A002375, A068307, A025583.

Sequence in context: A097849 A100678 A026834 * A176839 A179844 A076223

Adjacent sequences: A071332 A071333 A071334 * A071336 A071337 A071338

Keyword

nonn,look

Author

Reinhard Zumkeller, May 19 2002

Status

approved