This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A352753 #13 Apr 02 2022 18:35:56
%S A352753 0,4,10,10,20,20,51,34,51,68,112,112,164,123,164,205,290,232,385,308,
%T A352753 385,462,600,600,600,600,700,700,903,903,1280,1120,1120,1280,1280,
%U A352753 1440,1970,1773,1773,1970,2380,2380,2810,2529,2810,2810,3280,2952,3280,3280,3608
%N A352753 a(n) = (pi(2n-1) - pi(n-1)) * Sum_{p <= n, p prime} p.
%C A352753 Sum of the primes p from the ordered pairs of prime numbers, (p,q), such that p <= n <= q < 2n.
%F A352753 a(n) = A035250(n) * A034387(n). - _Bernard Schott_, Apr 02 2022
%F A352753 a(n) = A352775(n) - A352754(n).
%e A352753 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.
%t A352753 Table[(PrimePi[2 n - 1] - PrimePi[n - 1]) Sum[k (PrimePi[k] - PrimePi[k - 1]), {k, n}], {n, 100}]
%Y A352753 Cf. A000720 (pi), A034387, A035250, A352749, A352754, A352775, A352777.
%K A352753 nonn
%O A352753 1,2
%A A352753 _Wesley Ivan Hurt_, Apr 01 2022