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A169646
Number of squarefree numbers of form k*n, 1 <= k <= n.
1
1, 1, 2, 0, 3, 2, 5, 0, 0, 3, 7, 0, 8, 5, 6, 0, 11, 0, 12, 0, 8, 9, 15, 0, 0, 10, 0, 0, 17, 8, 19, 0, 13, 13, 15, 0, 23, 15, 17, 0, 26, 11, 28, 0, 0, 18, 30, 0, 0, 0, 21, 0, 32, 0, 25, 0, 23, 23, 36, 0, 37, 25, 0, 0, 30, 18, 41, 0, 29, 22, 44, 0, 45, 30, 0, 0, 36, 22, 49, 0, 0, 32, 51, 0, 41, 34
OFFSET
1,3
COMMENTS
a(n) = A008966(n)*A073311(n);
a(A000040(n)) = A112929(n).
LINKS
FORMULA
a(n) = Sum_{i=1..n} mu(n*i)^2, where mu is the Moebius function (A008683). - Ridouane Oudra, Jul 24 2019
MAPLE
seq(add(mobius(n*i)^2, i = 1 .. n), n = 1 .. 90); # Ridouane Oudra, Jul 24 2019
MATHEMATICA
Count[#, _?SquareFreeQ]&/@Table[k*n, {n, 90}, {k, n}] (* Harvey P. Dale, Sep 05 2012 *)
Table[Sum[MoebiusMu[i n]^2, {i, n}], {n, 100}] (* Vincenzo Librandi, Jul 25 2019 *)
PROG
(Magma) [&+[MoebiusMu(k*n)^2: k in [1..n]]: n in [1..80]]; // Vincenzo Librandi, Jul 25 2019
CROSSREFS
Sequence in context: A374018 A279591 A279675 * A349125 A231117 A021496
KEYWORD
nonn
AUTHOR
Reinhard Zumkeller, Apr 05 2010
STATUS
approved