%I
%S 0,1,0,1,1,0,1,1,1,0,1,1,1,1,0,1,1,1,1,1,0,1,2,2,1,1,0,0,2,2,2,1,2,0,
%T 0,0,3,3,3,1,2,0,0,0,0,4,4,3,2,2,0,0,0,0,0,7,4,3,3,2,0,0,0,0,0,0,7,4,
%U 3,4,3,0,0,0,0,0,0,0,7,4,3,4,3,0,0,0,0,0,0,0,0,7,7,4,4,3,0,0,0,0,0,0
%N T(n,k) = number of occurrences of kth prime in the first n partition numbers (with repetitions), 0<=k<n, triangular array read by rows.
%e Prime factorizations of the first 12 partition numbers:
%e P(0)=1, P(1)=1, P(2)=2, P(3)=3, P(4)=5, P(5)=7, P(6)=11, P(7)=15=5*3,
%e P(8)=22=11*2, P(9)=30=5*3*2, P(10)=42=7*3*2 and P(11)=56=7*2^3:
%e therefore T(11,1)=0+0+1+0+0+0+0+0+1+1+1+3=7 and T(11,2)=0+0+0+1+0+0+0+1+0+1+1+0=4.
%Y Cf. A000040, A000041.
%K nonn,tabl
%O 1,23
%A _Reinhard Zumkeller_, Feb 01 2004
