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

1,5

Comments

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

Links

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

Example

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

Mathematica

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

Crossrefs

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

Sequence in context: A360170 A306659 A191225 * A358009 A358010 A112022

Adjacent sequences: A223890 A223891 A223892 * A223894 A223895 A223896

Keyword

nonn

Author

Frank M Jackson, Mar 28 2013

Status

approved