Search: id:A119707
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%I A119707
%S A119707 0,1,1,1,3,2,4,3,4,4,5,4,6,5,6,6,7,6,8,7,8,8,9,8,9,9,9,9,10,9,11,10,11,
%T A119707 11,11,11,12,11,12,12,13,12,14,13,14,14,15,14,15,15,15,15,16,15,16,16,
%U A119707 16,16,17,16,18,17,18,18,18,18,19,18,19,19,20,19,21,20,21,21,21,21,22
%N A119707 Number of distinct primes appearing in all partitions of n into prime 
               parts.
%F A119707 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 A119707 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 A119707 There are 3 distinct primes involved in the partitions of 5 = 2+3, so 
               a(5) = 3.
%t A119707 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 A119707 Cf. A000720.
%Y A119707 Sequence in context: A130079 A134559 A007456 this_sequence A052938 A140114 
               A025532
%Y A119707 Adjacent sequences: A119704 A119705 A119706 this_sequence A119708 A119709 
               A119710
%K A119707 nonn
%O A119707 1,5
%A A119707 Anton Joha (antonjoha(AT)hotmail.com), Jun 10 2006
%E A119707 Edited and extended by Robert G. Wilson v (rgwv(at)rgwv.com), Jun 15 
               2006

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