A334229 Sum of the areas of all r X s rectangles such that r + s = 2n, with r, s composite.

0, 0, 0, 16, 24, 68, 88, 172, 289, 344, 400, 735, 680, 956, 1478, 1428, 1793, 2590, 2208, 3159, 4143, 4015, 4485, 6209, 6254, 6763, 8860, 8327, 9274, 13043, 10745, 13505, 16205, 14691, 18348, 21043, 19903, 22605, 26754, 25889, 27327, 35125, 30163, 34477, 44633

Offset

1,4

Links

Table of n, a(n) for n=1..45.

Formula

a(n) = Sum_{i=4..n} i * (2*n-i) * (1 - c(i)) * (1 - c(2*n-i)), where c is the prime characteristic (A010051).

Example

a(5) = 24; 2*5 = 10 has one rectangle with composite side lengths, 6 X 4 with area 24.
a(6) = 68; 2*6 = 12 has two rectangles with composite side lengths, 8 X 4 and 6 X 6, with total area 8*4 + 6*6 = 32 + 36 = 68.

Mathematica

Table[Sum[i (2 n - i) (1 - PrimePi[i] + PrimePi[i - 1]) (1 - PrimePi[2 n - i] + PrimePi[2 n - i - 1]), {i, 4, n}], {n, 50}]

Crossrefs

Cf. A010051.

Sequence in context: A029720 A204696 A024588 * A335296 A358447 A120468

Adjacent sequences: A334226 A334227 A334228 * A334230 A334231 A334232

Keyword

nonn,easy

Author

Wesley Ivan Hurt, Apr 19 2020

Status

approved