A223893 Number of partitions of n into at most three distinct primes.

0, 1, 1, 0, 2, 0, 2, 1, 1, 2, 1, 2, 2, 2, 2, 3, 1, 4, 3, 4, 3, 4, 3, 5, 3, 5, 3, 4, 4, 5, 6, 5, 5, 5, 5, 7, 6, 5, 7, 4, 7, 7, 8, 7, 7, 6, 10, 8, 9, 9, 8, 7, 12, 8, 12, 8, 10, 6, 14, 9, 15, 8, 13, 7, 14, 11, 16, 8, 14, 7, 19, 11, 19, 10, 15, 9, 21, 12, 20, 11, 18

Offset: 1

Author

Frank M Jackson, Mar 28 2013

Keywords

• nonn

Comments

The sequence shows a stronger version of the Goldbach conjecture that for n > 6, n has partitions with at most three distinct primes.

Examples

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

Links

• T. D. Noe, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A000586, A000607, A071335, A185101, A218007, A218469.

Programs

Mathematica

a[n_] := Length@Select[IntegerPartitions[n, 3, Prime@Range@PrimePi@n],
Sort@#==Union@# &]; Array[a, 100] (* Giovanni Resta, Mar 29 2013 *)