A303231 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.

0, 0, 0, 0, 15, 0, 105, 80, 315, 280, 0, 168, 1287, 1232, 2145, 3136, 0, 2664, 4845, 6320, 6783, 11176, 0, 11088, 12075, 17888, 0, 14448, 0, 17640, 24273, 27776, 29667, 62560, 0, 61632, 0, 28272, 50505, 76720, 0, 99120, 68757, 141944, 79335, 163024, 0

Offset

1,5

Links

Table of n, a(n) for n=1..47.

Index entries for sequences related to partitions

Formula

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).

Mathematica

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}]

Prog

(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

Crossrefs

Cf. A010051, A028723, A112742.

Sequence in context: A186436 A054670 A277929 * A225346 A225312 A370335

Adjacent sequences: A303228 A303229 A303230 * A303232 A303233 A303234

Keyword

nonn,easy

Author

Wesley Ivan Hurt, Apr 20 2018

Status

approved