A352754 - OEIS

%I #15 Apr 02 2022 18:36:04

%S 0,5,16,24,36,54,124,96,164,240,300,360,432,354,528,714,833,714,1112,

%T 960,1288,1632,1836,2052,2052,2052,2529,2529,2810,3110,4092,3751,3751,

%U 4488,4488,5269,6624,6180,6180,7128,7722,8268,8904,8302,9548,9548,10230,9525,10980,10980

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

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

%F a(n) = A000720(n) * A073837(n). - _Bernard Schott_, Apr 02 2022

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

%e 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.

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

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

%K nonn

%O 1,2

%A _Wesley Ivan Hurt_, Apr 01 2022