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%I #6 Apr 22 2018 17:45:15
%S 0,0,0,0,3,0,15,10,35,28,0,14,99,88,143,196,0,148,255,316,323,508,0,
%T 462,483,688,0,516,0,588,783,868,899,1840,0,1712,0,744,1295,1918,0,
%U 2360,1599,3226,1763,3544,0,4714,2115,4876,0,3378,0,5392,2703,4606,0
%N Total area of the family of rectangles with dimensions q and |q-p| such that p and q are prime, n = p + q and p < q.
%H <a href="/index/Par#part">Index entries for sequences related to partitions</a>
%F a(n) = Sum_{i=1..floor((n-1)/2)} (n-i) * (n-2i) * A010051(i) * A010051(n-i).
%t Table[Sum[(n - i) (n - 2 i) (PrimePi[i] - PrimePi[i - 1]) (PrimePi[n - i] - PrimePi[n - i - 1]), {i, Floor[(n - 1)/2]}], {n, 80}]
%o (PARI) a(n) = sum(i=1, (n-1)\2, (n-i)*(n-2*i)*isprime(i)*isprime(n-i)); \\ _Michel Marcus_, Apr 21 2018
%Y Cf. A010051, A303231.
%K nonn,easy
%O 1,5
%A _Wesley Ivan Hurt_, Apr 20 2018
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