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%I #8 May 31 2021 19:05:05
%S 0,0,1,2,4,4,8,10,14,15,21,21,27,31,36,42,48,46,58,61,68,73,83,83,96,
%T 100,110,114,127,123,144,146,157,165,175,179,201,201,212,221,241,235,
%U 258,265,275,282,303,301,328,330,346,351,381,377,403,406,427,433,455,452,486,493
%N a(n) is the number of primes in an n X n square array that do not appear on its border, with the elements of the square array being the numbers from 1..n^2, listed in increasing order by rows.
%F a(n) = pi(n*(n-1)) - pi(n) - Sum_{k=1..n-2} (pi(n*k+1) - pi(n*k)).
%e [1 2 3 4 5]
%e [1 2 3 4] [6 7 8 9 10]
%e [1 2 3] [5 6 7 8] [11 12 13 14 15]
%e [1 2] [4 5 6] [9 10 11 12] [16 17 18 19 20]
%e [1] [3 4] [7 8 9] [13 14 15 16] [21 22 23 24 25]
%e ------------------------------------------------------------------------
%e n 1 2 3 4 5
%e ------------------------------------------------------------------------
%e a(n) 0 0 1 2 4
%e ------------------------------------------------------------------------
%e primes {} {} {5} {7,11} {7,13,17,19}
%e ------------------------------------------------------------------------
%t Table[PrimePi[n*(n - 1)] - PrimePi[n] - Sum[PrimePi[n*k + 1] - PrimePi[n*k], {k, n - 2}], {n, 100}]
%Y Cf. A000720 (pi), A038107, A221490, A344316 (on border), A344349.
%K nonn
%O 1,4
%A _Wesley Ivan Hurt_, May 18 2021