cp's OEIS Frontend

A089818 T(n,k) = number of subsets of {1,..., n} containing exactly k primes, triangle read by rows, 0<=k

%I A089818 #8 Nov 04 2020 09:38:07
%S A089818 2,2,2,2,4,2,4,8,4,0,4,12,12,4,0,8,24,24,8,0,0,8,32,48,32,8,0,0,16,64,
%T A089818 96,64,16,0,0,0,32,128,192,128,32,0,0,0,0,64,256,384,256,64,0,0,0,0,0,
%U A089818 64,320,640,640,320,64,0,0,0,0,0,128,640,1280,1280,640,128,0,0,0,0,0
%N A089818 T(n,k) = number of subsets of {1,..., n} containing exactly k primes, triangle read by rows, 0<=k<n.
%C A089818 T(n,k) = T(n, A000720(n)-k) for 0<=k<=A000720(n);
%C A089818 T(n,k) = 0 iff k > A000720(n);
%C A089818 A089819(n) = T(n,0); A089821(n) = T(n,1) for n>1; A089822(n) = T(n,2) for n>2;
%C A089818 A089820(n) = Sum(T(n,k): 1<=k<=A000720(n));
%C A089818 T(n,k) = A007318(A000720(n),k) * A000079(n-A000720(n)).
%F A089818 T(n, k) = binomial(pi(n), k)*2^(n-pi(n)), with pi = A000720.
%t A089818 T[n_, k_] := Binomial[PrimePi[n], k] 2^(n - PrimePi[n]);
%t A089818 Table[T[n, k], {n, 1, 12}, {k, 0, n-1}] // Flatten (* _Jean-François Alcover_, Nov 04 2020 *)
%Y A089818 Cf. A000040.
%K A089818 nonn,tabl
%O A089818 1,1
%A A089818 _Reinhard Zumkeller_, Nov 12 2003