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%I #2 Mar 30 2012 17:34:20
%S 1,3,3,7,7,11,11,11,11,13,13,17,17,17,17,23,23,29,29,29,29,33,33,33,
%T 33,33,33,35,35,49,49,49,49,49,49,55,55,55,55,61,61,71,71,71,71,83,83,
%U 83,83,83,83,85,85,85,85,85,85,91,91,93,93,93,93,93,93,107,107,107,107,111
%N Sum([pi(j+1)-pi(j)][prime(j+1)-prime(j)],j=1..n), where pi(k) is the number of prime numbers less than or equal to k and prime(k) is the k-th prime.
%e a(2)=3 because pi(1)=0,p(2)=1,p(3)=2,prime(1)=2,prime(2)=3,prime(3)=5 and so a(2)=(1-0)(3-2)+(2-1)(5-3)=1+2=3.
%p with(numtheory): a:=n->sum((pi(k+1)-pi(k))*(ithprime(k+1)-ithprime(k)),k=1..n): seq(a(n),n=1..70);
%t an = Table[(PrimePi[n + 1] - PrimePi[n])*(Prime[n + 1] - Prime[n]), {n, 1, 200}] a[0] = 0; a[n_] := a[n] = a[n - 1] + an[[n]] aa = Table[a[n], {n, 0, Length[an]}]
%Y Cf. A001223, A010051.
%Y Partial sums of A109578.
%K nonn
%O 1,2
%A _Roger L. Bagula_, Jun 29 2005
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