Search: id:A037032
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%I A037032
%S A037032 0,1,2,4,7,13,20,32,48,73,105,153,214,302,415,569,767,1034,1371,1817,
%T A037032 2380,3110,4025,5199,6659,8512,10806,13684,17229,21645,27049,33728,
%U A037032 41872,51863,63988,78779,96645,118322,144406,175884,213617,258957
%N A037032 Total number of prime parts in all partitions of n.
%F A037032 a(n) = Sum_{k=1..n} A001221(k)*A000041(n-k). - Vladeta Jovovic (vladeta(AT)eunet.rs), 
               Aug 22 2002
%e A037032 p(3) = 1+1+1, 1+2, 3 -> {2, 3} = 2
%p A037032 with(combinat): a:=proc(n) local P,c,j,i: P:=partition(n): c:=0: for 
               j from 1 to numbpart(n) do for i from 1 to nops(P[j]) do if isprime(P[j][i])=true 
               then c:=c+1 else c:=c fi: od: od: c: end: seq(a(n),n=1..42); - Emeric 
               Deutsch (deutsch(AT)duke.poly.edu), Mar 30 2006
%Y A037032 Cf. A000041.
%Y A037032 Sequence in context: A109853 A127977 A112997 this_sequence A165753 A090752 
               A051058
%Y A037032 Adjacent sequences: A037029 A037030 A037031 this_sequence A037033 A037034 
               A037035
%K A037032 nonn
%O A037032 1,3
%A A037032 G. L. Honaker, Jr. (honak3r(AT)gmail.com)
%E A037032 More terms from Naohiro Nomoto (n_nomoto(AT)yabumi.com), Apr 19 2002

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