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

1,2

Links

Table of n, a(n) for n=1..73.

Formula

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

Example

                                                      [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}
------------------------------------------------------------------------

Mathematica

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

Crossrefs

Cf. A008683 (mu), A209297.

Sequence in context: A243285 A085972 A136378 * A305557 A099249 A050296

Adjacent sequences: A344371 A344372 A344373 * A344375 A344376 A344377

Keyword

nonn

Author

Wesley Ivan Hurt, May 17 2021

Status

approved