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%I #6 May 15 2021 23:13:05
%S 1,2,3,3,4,5,6,5,6,8,10,8,10,10,13,11,14,12,16,13,17,16,18,15,18,18,
%T 23,20,25,18,27,19,26,24,30,23,33,25,30,28,32,27,39,28,36,33,39,30,41,
%U 32,45,38,44,33,51,37,45,40,49,37,54,36,51,45,54,43,61,41,57,48,59,46,64
%N a(n) = Sum_{k=1..n} mu(n*k-k-1)^2, where mu is the Möbius function.
%C Number of squarefree numbers along the main antidiagonal of the n X n square array whose elements are the numbers from 1..n^2, listed in increasing order by rows.
%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) 1 2 3 3 4
%e ------------------------------------------------------------------------
%e numbers {1} {2,3} {3,5,7} {7,10,13} {5,13,17,21}
%e ------------------------------------------------------------------------
%t Table[Sum[MoebiusMu[n*k - k + 1]^2, {k, n}], {n, 100}]
%Y Cf. A008683 (Möbius).
%K nonn
%O 1,2
%A _Wesley Ivan Hurt_, May 15 2021