%I
%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(n2) = A000720(n2)
%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
