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%I #11 Sep 17 2020 16:43:15
%S 0,0,0,0,15,0,105,80,315,280,0,168,1287,1232,2145,3136,0,2664,4845,
%T 6320,6783,11176,0,11088,12075,17888,0,14448,0,17640,24273,27776,
%U 29667,62560,0,61632,0,28272,50505,76720,0,99120,68757,141944,79335,163024,0
%N Total volume of all rectangular prisms with dimensions q, p+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) = n * Sum_{i=1..floor((n-1)/2)} (n-i) * (n-2*i) * c(i) * c(n-i), where c is the prime characteristic (A010051).
%t Table[n*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) = 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, A028723, A112742.
%K nonn,easy
%O 1,5
%A _Wesley Ivan Hurt_, Apr 20 2018
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