A073312 Number of nonsquarefree numbers in the reduced residue system of n.

0, 0, 0, 0, 1, 0, 1, 0, 2, 1, 3, 0, 4, 1, 2, 1, 5, 0, 6, 1, 4, 1, 7, 0, 7, 2, 5, 3, 11, 0, 11, 3, 7, 3, 9, 1, 13, 3, 7, 2, 14, 1, 14, 3, 6, 4, 16, 1, 16, 3, 11, 5, 20, 2, 15, 4, 13, 5, 22, 1, 23, 5, 10, 6, 18, 2, 25, 6, 15, 2, 26, 2, 27, 6, 11, 7, 24, 2, 29, 4, 17, 8, 31, 1, 23, 8, 17, 8, 33, 1, 28

Offset: 1

Author

Reinhard Zumkeller, Jul 25 2002

Keywords

• nonn

Examples

			n=15, there are A000010(15)=8 residues: 1, 2, 4=2^2, 7, 8=2^3, 11, 13 and 14; two of them are not squarefree: 4 and 8, therefore a(15)=2.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A073311, A013929, A000010, A048864, A048865.

Cf. A065463, A104141.

Programs

Mathematica

a[n_] := EulerPhi[n] - Module[{rad = Times @@ (First@# & /@ FactorInteger[n])}, Sum[MoebiusMu[k*rad]^2, {k, 1, n}]]; Array[a, 100] (* Amiram Eldar, Mar 08 2020 *)

Formula

a(n) + A073311(n) = A000010(n).

Sum_{k=1..n} a(k) ~ c * n^2, where c = (3/Pi^2) * (1 - A065463) = 0.0898387... . - Amiram Eldar, Dec 07 2023