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

1,5

Links

Table of n, a(n) for n=1..57.

Index entries for sequences related to partitions

Formula

a(n) = Sum_{i=1..floor((n-1)/2)} (n-i) * (n-2i) * A010051(i) * A010051(n-i).

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}]

Prog

(PARI) a(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, A303231.

Sequence in context: A365419 A366410 A054882 * A086479 A091000 A361804

Adjacent sequences: A303229 A303230 A303231 * A303233 A303234 A303235

Keyword

nonn,easy

Author

Wesley Ivan Hurt, Apr 20 2018

Status

approved