A303232 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.
0, 0, 0, 0, 3, 0, 15, 10, 35, 28, 0, 14, 99, 88, 143, 196, 0, 148, 255, 316, 323, 508, 0, 462, 483, 688, 0, 516, 0, 588, 783, 868, 899, 1840, 0, 1712, 0, 744, 1295, 1918, 0, 2360, 1599, 3226, 1763, 3544, 0, 4714, 2115, 4876, 0, 3378, 0, 5392, 2703, 4606, 0
Offset: 1
Programs
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Mathematica
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}] -
PARI
a(n) = sum(i=1, (n-1)\2, (n-i)*(n-2*i)*isprime(i)*isprime(n-i)); \\ Michel Marcus, Apr 21 2018