

A223893


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


2



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
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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: A035226 A126043 A191225 * A112022 A000586 A029399
Adjacent sequences: A223890 A223891 A223892 * A223894 A223895 A223896


KEYWORD

nonn


AUTHOR

Frank M Jackson, Mar 28 2013


STATUS

approved



