A352777 a(n) = Sum_{p <= n <= q < 2n, p,q prime} (p * q).

0, 10, 40, 60, 120, 180, 527, 408, 697, 1020, 1680, 2016, 2952, 2419, 3608, 4879, 6902, 5916, 10703, 9240, 12397, 15708, 20400, 22800, 22800, 22800, 28100, 28100, 36249, 40119, 59520, 54560, 54560, 65280, 65280, 76640, 108744, 101455, 101455, 117018, 141372, 151368, 178716

Offset: 1

Author

Wesley Ivan Hurt, Apr 02 2022

Keywords

• nonn

Comments

Total area of all unique p X q rectangles with p,q prime such that p <= n <= q < 2n.

Examples

			a(5) = 120; the 6 unique p X q rectangles, with p,q prime such that p <= 5 <= q < 10 are: 2 X 5, 2 X 7, 3 X 5, 3 X 7, 5 X 5, and 5 X 7. The total area of all rectangles is 2*5 + 2*7 + 3*5 + 3*7 + 5*5 + 5*7 = 120.
		

Crossrefs

Cf. A000720 (pi), A035250, A352753, A352754, A352749.

Programs

Mathematica

Table[Sum[Sum[k (2 n - i) (PrimePi[k] - PrimePi[k - 1]) (PrimePi[2 n - i] - PrimePi[2 n - i - 1]), {k, n}], {i, n}], {n, 100}]