A344350 a(n) = Sum_{k=1..n} mu(n*k-k-1)^2, where mu is the Möbius function.

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, 23, 20, 25, 18, 27, 19, 26, 24, 30, 23, 33, 25, 30, 28, 32, 27, 39, 28, 36, 33, 39, 30, 41, 32, 45, 38, 44, 33, 51, 37, 45, 40, 49, 37, 54, 36, 51, 45, 54, 43, 61, 41, 57, 48, 59, 46, 64

Offset

1,2

Comments

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.

Links

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

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         3            3                 4
------------------------------------------------------------------------
  numbers  {1}      {2,3}    {3,5,7}     {7,10,13}       {5,13,17,21}
------------------------------------------------------------------------

Mathematica

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

Crossrefs

Cf. A008683 (Möbius).

Sequence in context: A244041 A331835 A022290 * A185363 A103827 A094182

Adjacent sequences: A344347 A344348 A344349 * A344351 A344352 A344353

Keyword

nonn

Author

Wesley Ivan Hurt, May 15 2021

Status

approved