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%I #17 May 27 2021 13:44:26
%S 3,5,7,11,24,30,36,59,42,52,83,60,97,138,152,168,168,221,184,243,263,
%T 220,287,311,384,384,410,493,493,523,462,462,559,593,696,732,768,881,
%U 881,802,802,719,846,977,888,1025,1164,1164,1067,1216,1266,1163,1320,1213,1267,1434
%N Sum of the prime numbers in the interval (2n, 3n].
%C For n >= 3, a(n) is the sum of the prime numbers appearing in the 3rd row of an n X n square array whose elements are the numbers from 1..n^2, listed in increasing order by rows.
%F a(n) = Sum_{k=2*n+1..3*n} k * (pi(k) - pi(k-1)).
%e [1 2 3 4 5 6]
%e [1 2 3 4 5] [7 8 9 10 11 12]
%e [1 2 3 4] [6 7 8 9 10] [13 14 15 16 17 18]
%e [1 2 3] [5 6 7 8] [11 12 13 14 15] [19 20 21 22 23 24]
%e [4 5 6] [9 10 11 12] [16 17 18 19 20] [25 26 27 28 29 30]
%e [7 8 9] [13 14 15 16] [21 22 23 24 25] [31 32 33 34 35 36]
%e ----------------------------------------------------------------------------
%e n 3 4 5 6
%e ----------------------------------------------------------------------------
%e a(n) 7 11 24 30
%e ----------------------------------------------------------------------------
%t Table[Sum[k*(PrimePi[k] - PrimePi[k - 1]), {k, 2 n + 1, 3 n}], {n, 80}]
%Y Cf. A000720 (pi), A108954.
%K nonn
%O 1,1
%A _Wesley Ivan Hurt_, May 17 2021
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