A352754 a(n) = pi(n) * Sum_{n <= q < 2n, q prime} q.

0, 5, 16, 24, 36, 54, 124, 96, 164, 240, 300, 360, 432, 354, 528, 714, 833, 714, 1112, 960, 1288, 1632, 1836, 2052, 2052, 2052, 2529, 2529, 2810, 3110, 4092, 3751, 3751, 4488, 4488, 5269, 6624, 6180, 6180, 7128, 7722, 8268, 8904, 8302, 9548, 9548, 10230, 9525, 10980, 10980

Offset: 1

Author

Wesley Ivan Hurt, Apr 01 2022

Keywords

• nonn

Comments

Sum of the primes q from the ordered pairs of prime numbers, (p,q), such that p <= n <= q < 2n.

Examples

			a(5) = 36; there are 6 ordered pairs of prime numbers, (p,q), such that p <= 5 <= q < 10: (2,5), (2,7), (3,5), (3,7), (5,5), and (5,7). The sum of the corresponding prime parts q gives 5+7+5+7+5+7 = 36.
		

Crossrefs

Cf. A000720 (pi), A073837, A352749, A352753, A352775, A352777.

Programs

Mathematica

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

Formula

a(n) = A000720(n) * A073837(n). - Bernard Schott, Apr 02 2022

a(n) = A352775(n) - A352753(n).