A341700 Sum of the primes p satisfying n < p <= 2n.

2, 3, 5, 12, 7, 18, 24, 24, 41, 60, 49, 72, 59, 59, 88, 119, 102, 102, 120, 120, 161, 204, 181, 228, 228, 228, 281, 281, 252, 311, 341, 341, 341, 408, 408, 479, 515, 515, 515, 594, 553, 636, 593, 593, 682, 682, 635, 635, 732, 732, 833, 936, 883, 990, 1099, 1099

Offset: 1

Author

Chai Wah Wu, Feb 17 2021

Keywords

• nonn

Comments

For n >= 2, a(n) is the sum of the prime numbers appearing in the 2nd row of an n X n square array whose elements are the numbers from 1..n^2, listed in increasing order by rows. - Wesley Ivan Hurt, May 17 2021

Examples

			a(7) = 24 = 11+13 (sum of primes larger than 7 and less than or equal to 14).
		

Crossrefs

Cf. A010051, A034387, A073837, A108954, A128076.

Programs

Mathematica

Array[Total@ Select[Range[# + 1, 2 #], PrimeQ] &, 56] (* Michael De Vlieger, Feb 17 2021 *)

Python

from sympy import nextprime
def A341700(n):
    s, m = 0, nextprime(n)
    while m <= 2*n:
        s += m
        m = nextprime(m)
    return s

Formula

a(n) = A034387(2*n) - A034387(n).

a(n) = A073837(n) if n is not a prime. Otherwise, a(n) = A073837(n)-n.

For n >= 2, a(n) = Sum_{k=(n^2-n+2)/2..(n^2+n-2)/2} A010051(A128076(k)) * A128076(k). - Wesley Ivan Hurt, Jan 08 2022