%I #5 Oct 31 2013 12:17:39

%S 0,1,1,1,3,2,4,3,4,4,5,4,6,5,6,6,7,6,8,7,8,8,9,8,9,9,9,9,10,9,11,10,

%T 11,11,11,11,12,11,12,12,13,12,14,13,14,14,15,14,15,15,15,15,16,15,16,

%U 16,16,16,17,16,18,17,18,18,18,18,19,18,19,19,20,19,21,20,21,21,21,21,22

%N Number of distinct primes appearing in all partitions of n into prime parts.

%F When n = odd and >=5 then a(n) = pi(n) = A000720(n). When n = even and >=4 then a(n) = pi(n-2) = A000720(n-2)

%e There is only 1 distinct prime number involved in the partitions of 4, namely 2 (in 2+2 = 4). The partition 3+1 does not count, as 1 is not a prime. So a(4)= 1.

%e There are 3 distinct primes involved in the partitions of 5 = 2+3, so a(5) = 3.

%t f[n_] := If[OddQ@n, If[n == 3, 1, PrimePi@n], If[n == 2, 1, PrimePi[n - 2]]]; Array[f, 80] (* _Robert G. Wilson v_ *)

%Y Cf. A000720.

%K nonn

%O 1,5

%A _Anton Joha_, Jun 10 2006

%E Edited and extended by _Robert G. Wilson v_, Jun 15 2006