cp's OEIS Frontend

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

%I A341700 #17 Jan 08 2022 23:04:47
%S A341700 2,3,5,12,7,18,24,24,41,60,49,72,59,59,88,119,102,102,120,120,161,204,
%T A341700 181,228,228,228,281,281,252,311,341,341,341,408,408,479,515,515,515,
%U A341700 594,553,636,593,593,682,682,635,635,732,732,833,936,883,990,1099,1099
%N A341700 Sum of the primes p satisfying n < p <= 2n.
%C A341700 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
%F A341700 a(n) = A034387(2*n) - A034387(n).
%F A341700 a(n) = A073837(n) if n is not a prime. Otherwise, a(n) = A073837(n)-n.
%F A341700 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
%e A341700 a(7) = 24 = 11+13 (sum of primes larger than 7 and less than or equal to 14).
%t A341700 Array[Total@ Select[Range[# + 1, 2 #], PrimeQ] &, 56] (* _Michael De Vlieger_, Feb 17 2021 *)
%o A341700 (Python)
%o A341700 from sympy import nextprime
%o A341700 def A341700(n):
%o A341700     s, m = 0, nextprime(n)
%o A341700     while m <= 2*n:
%o A341700         s += m
%o A341700         m = nextprime(m)
%o A341700     return s
%Y A341700 Cf. A010051, A034387, A073837, A108954, A128076.
%K A341700 nonn
%O A341700 1,1
%A A341700 _Chai Wah Wu_, Feb 17 2021