%I A117278
%S A117278 1,1,0,1,1,1,0,1,1,1,1,1,0,1,1,1,0,1,2,1,0,2,1,1,1,1,0,2,2,1,0,1,2,2,1,
%T A117278 1,1,1,2,2,2,1,0,2,1,3,2,1,1,0,1,3,2,3,2,1,0,2,2,3,3,2,1,1,1,0,4,3,3,3,
%U A117278 2,1,0,2,2,4,3,4,2,1,1,1,1,3,4,5,3,3,2,1,0,2,2,6,4,4,4,2,1,1,0,1,5,3,6
%N A117278 Triangle read by rows: T(n,k) is the number of partitions of n into k 
               prime parts (n>=2, 1<=k<=floor(n/2)).
%C A117278 Row n has floor(n/2) terms. Row sums yield A000607. T(n,1)=A010051(n) 
               (the characteristic function of the primes). T(n,2)=A061358(n). Sum(k*T(n,
               k),k>=1) = A084993(n).
%F A117278 G.f.=G(t,x)=-1+1/product(1-tx^(p(j)), j=1..infinity), where p(j) is the 
               j-th prime.
%e A117278 T(12,3)=2 because we have [7,3,2] and [5,5,2].
%e A117278 Triangle starts:
%e A117278 1;
%e A117278 1;
%e A117278 0,1;
%e A117278 1,1;
%e A117278 0,1,1;
%e A117278 1,1,1;
%e A117278 0,1,1,1;
%e A117278 0,1,2,1;
%p A117278 g:=1/product(1-t*x^(ithprime(j)),j=1..30): gser:=simplify(series(g,x=0,
               30)): for n from 2 to 22 do P[n]:=sort(coeff(gser,x^n)) od: for n 
               from 2 to 22 do seq(coeff(P[n],t^j),j=1..floor(n/2)) od; # yields 
               sequence in triangular form
%Y A117278 Cf. A000607, A010051, A061358, A084993.
%Y A117278 Sequence in context: A024361 A135486 A030187 this_sequence A140082 A025852 
               A025846
%Y A117278 Adjacent sequences: A117275 A117276 A117277 this_sequence A117279 A117280 
               A117281
%K A117278 nonn,tabf
%O A117278 2,19
%A A117278 Emeric Deutsch (deutsch(AT)duke.poly.edu), Mar 07 2006