A076545 a(n) = Sum_{k=1..n} (mu(k) + sqf(k)) where mu(k) is Moebius function, sqf(k)=1 if k is squarefree and sqf(k)=-1 otherwise.

2, 2, 2, 1, 1, 3, 3, 2, 1, 3, 3, 2, 2, 4, 6, 5, 5, 4, 4, 3, 5, 7, 7, 6, 5, 7, 6, 5, 5, 5, 5, 4, 6, 8, 10, 9, 9, 11, 13, 12, 12, 12, 12, 11, 10, 12, 12, 11, 10, 9, 11, 10, 10, 9, 11, 10, 12, 14, 14, 13, 13, 15, 14, 13, 15, 15, 15, 14, 16, 16, 16, 15, 15, 17, 16, 15, 17, 17, 17, 16, 15

Offset

1,1

Links

Table of n, a(n) for n=1..81.

Formula

a(n) = Sum_{k=1..n} (2*mu(k)^2 + mu(k) - 1), where mu = A008683. - Wesley Ivan Hurt, Feb 12 2026

Mathematica

Accumulate[Table[MoebiusMu[n]+If[SquareFreeQ[n], 1, -1], {n, 100}]] (* Harvey P. Dale, Jun 02 2022 *)

Crossrefs

Partial sums of A076544.

Cf. A008683 (mu).

Sequence in context: A098593 A144431 A053821 * A162246 A277447 A333698

Adjacent sequences: A076542 A076543 A076544 * A076546 A076547 A076548

Keyword

easy,nonn

Author

Zak Seidov, Oct 19 2002

Status

approved