A352753 a(n) = (pi(2n-1) - pi(n-1)) * Sum_{p <= n, p prime} p.

0, 4, 10, 10, 20, 20, 51, 34, 51, 68, 112, 112, 164, 123, 164, 205, 290, 232, 385, 308, 385, 462, 600, 600, 600, 600, 700, 700, 903, 903, 1280, 1120, 1120, 1280, 1280, 1440, 1970, 1773, 1773, 1970, 2380, 2380, 2810, 2529, 2810, 2810, 3280, 2952, 3280, 3280, 3608

Offset

1,2

Comments

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

Links

Table of n, a(n) for n=1..51.

Formula

a(n) = A035250(n) * A034387(n). - Bernard Schott, Apr 02 2022

a(n) = A352775(n) - A352754(n).

Example

a(5) = 20; 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 p gives 2+2+3+3+5+5 = 20.

Mathematica

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

Crossrefs

Cf. A000720 (pi), A034387, A035250, A352749, A352754, A352775, A352777.

Sequence in context: A180862 A310334 A310335 * A310336 A227060 A278727

Adjacent sequences: A352750 A352751 A352752 * A352754 A352755 A352756

Keyword

nonn

Author

Wesley Ivan Hurt, Apr 01 2022

Status

approved