A344374 a(n) is the number of squarefree numbers appearing in the 1st column of an n X n square array whose elements are the numbers from 1..n^2, listed in increasing order by rows.

1, 2, 2, 3, 4, 5, 5, 5, 7, 9, 7, 9, 9, 12, 10, 13, 11, 17, 12, 16, 15, 18, 14, 17, 17, 22, 19, 24, 17, 27, 18, 26, 23, 29, 22, 32, 24, 30, 27, 31, 27, 38, 28, 35, 32, 38, 29, 40, 31, 44, 37, 43, 32, 50, 36, 44, 40, 48, 36, 53, 35, 50, 44, 53, 42, 60, 41, 58, 47, 59, 45, 63, 45

Offset: 1

Author

Wesley Ivan Hurt, May 17 2021

Keywords

• nonn

Examples

			                                                      [1   2  3  4  5]
                                      [1   2  3  4]   [6   7  8  9 10]
                            [1 2 3]   [5   6  7  8]   [11 12 13 14 15]
                   [1 2]    [4 5 6]   [9  10 11 12]   [16 17 18 19 20]
           [1]     [3 4]    [7 8 9]   [13 14 15 16]   [21 22 23 24 25]
------------------------------------------------------------------------
  n         1        2         3            4                 5
------------------------------------------------------------------------
  a(n)      1        2         2            3                 4
------------------------------------------------------------------------
  numbers  {1}     {1,3}     {1,7}       {1,5,13}        {1,6,11,21}
------------------------------------------------------------------------
		

Crossrefs

Cf. A008683 (mu), A209297.

Programs

Mathematica

Table[Sum[MoebiusMu[1 + n (k - 1)]^2, {k, n}], {n, 100}]

Formula

a(n) = Sum_{k=1..n} mu(1+n*(k-1))^2, where mu is the Möbius function.