%I #6 May 31 2021 19:41:27
%S 1,1,2,3,4,4,4,6,8,6,8,8,11,9,12,10,16,12,15,14,17,14,16,16,21,18,23,
%T 16,26,18,25,22,28,21,31,23,29,26,30,26,37,27,34,31,37,28,39,30,43,36,
%U 42,31,49,35,43,39,47,35,52,34,49,43,52,41,59,40,58,47,58,44,62,44,60
%N Number of squarefree numbers along the main diagonal of an n X n square array whose elements are the numbers from 1..n^2, listed in increasing order by rows.
%C Number of squarefree numbers along the main diagonal 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=1..n} mu(n*k-n+k)^2, where mu is the Möbius function.
%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 1 2 3 4
%e ------------------------------------------------------------------------
%e numbers {1} {1} {1,5} {1,6,11} {1,7,13,19}
%e ------------------------------------------------------------------------
%t Table[Sum[MoebiusMu[n*(k - 1) + k]^2, {k, n}], {n, 100}]
%Y Cf. A008683 (Möbius), A344350.
%K nonn
%O 1,3
%A _Wesley Ivan Hurt_, May 15 2021