A352775 a(n) = pi(n) * (Sum_{n <= q < 2n, q prime} q) + (pi(2n-1) - pi(n-1)) * (Sum_{p <= n, p prime} p).

0, 9, 26, 34, 56, 74, 175, 130, 215, 308, 412, 472, 596, 477, 692, 919, 1123, 946, 1497, 1268, 1673, 2094, 2436, 2652, 2652, 2652, 3229, 3229, 3713, 4013, 5372, 4871, 4871, 5768, 5768, 6709, 8594, 7953, 7953, 9098, 10102, 10648, 11714, 10831, 12358, 12358, 13510

Offset

1,2

Comments

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

Links

Table of n, a(n) for n=1..47.

Formula

a(n) = A352753(n) + A352754(n).

Example

a(5) = 56; 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 all the parts gives 2+5+2+7+3+5+3+7+5+5+5+7 = 56.

Mathematica

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

Crossrefs

Cf. A000720 (pi), A073837, A352749, A352753, A352754, A352777.

Sequence in context: A255107 A022421 A075395 * A085367 A343560 A330395

Adjacent sequences: A352772 A352773 A352774 * A352776 A352777 A352778

Keyword

nonn

Author

Wesley Ivan Hurt, Apr 02 2022

Status

approved