A303223 Sum of the perimeters of the family of rectangles with dimensions p and q such that |q - p| is prime, n = p + q and p < q.

0, 0, 0, 8, 10, 12, 28, 16, 54, 20, 66, 24, 104, 28, 150, 32, 170, 36, 228, 40, 294, 44, 322, 48, 400, 52, 432, 56, 464, 60, 558, 64, 660, 68, 700, 72, 740, 76, 858, 80, 902, 84, 1032, 88, 1170, 92, 1222, 96, 1372, 100, 1428, 104, 1484, 108, 1650, 112, 1710

Offset: 1

Author

Wesley Ivan Hurt, Apr 19 2018

Keywords

• nonn
• easy

Links

• Index entries for sequences related to partitions

Crossrefs

Cf. A010051, A294247.

Programs

Mathematica

Table[2 n*Sum[(PrimePi[n - 2 i] - PrimePi[n - 2 i - 1]), {i, Floor[(n - 1)/2]}], {n, 80}]

PARI

a(n) = 2*n*sum(i=1, (n-1)\2, isprime(n-2*i)); \\ Michel Marcus, Apr 21 2018

Formula

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