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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.
0
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
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
KEYWORD
nonn
AUTHOR
Wesley Ivan Hurt, May 17 2021
STATUS
approved