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A096066 Triangle read by rows, 1<=k<=n: T(n,k) is the number of occurrences of the k-th prime in partitions of the n-th prime into primes.

%I A096066 #13 Sep 23 2021 05:08:38
%S A096066 1,0,1,1,1,1,3,1,1,1,10,6,2,1,1,16,9,4,2,1,1,37,22,11,6,2,1,1,54,32,
%T A096066 15,9,3,2,1,1,107,65,32,19,7,5,2,1,1,266,165,84,50,22,15,7,5,2,1,353,
%U A096066 219,112,69,30,21,10,7,3,1,1,779,487,254,157,73,52,27,19,10,3,2,1,1270,795,420,261,124,90,49,36,19,7,5,1,1
%N A096066 Triangle read by rows, 1<=k<=n: T(n,k) is the number of occurrences of the k-th prime in partitions of the n-th prime into primes.
%F A096066 T(n,n) = 1.
%e A096066 n=5, A000040(5)=11 with A056768(5)=6 partitions into primes:
%e A096066 T(5,1)=10 prime(1)=2 in 7+2+2=5+2+2+2=3+3+3+2=3+2+2+2+2,
%e A096066 T(5,2)=6 prime(2)=3: in 5+3+3=3+3+3+2=3+2+2+2+2,
%e A096066 T(5,3)=2 prime(3)=5: in 5+3+3=5+2+2+2,
%e A096066 T(5,4)=1 prime(4)=7: in 7+2+2.
%e A096066 Triangle begins:
%e A096066   1;
%e A096066   0,  1;
%e A096066   1,  1, 1;
%e A096066   3,  1, 1, 1;
%e A096066   10, 6, 2, 1, 1;
%e A096066   ...
%t A096066 ip[p_] := ip[p] = IntegerPartitions[p, All, Select[Range[p], PrimeQ]] // Flatten;
%t A096066 T[n_, k_] := Count[ip[Prime[n]], Prime[k]];
%t A096066 Table[T[n, k], {n, 1, 13}, {k, 1, n}] // Flatten (* _Jean-François Alcover_, Sep 23 2021 *)
%Y A096066 Cf. A056768.
%K A096066 nonn,tabl
%O A096066 1,7
%A A096066 _Reinhard Zumkeller_, Jul 21 2004
%E A096066 Name modified by _Jean-François Alcover_, Sep 23 2021