A247418 a(n) = Sum_{i=1..n} mu(i)*(-1)^(i+1).

1, 2, 1, 1, 0, -1, -2, -2, -2, -3, -4, -4, -5, -6, -5, -5, -6, -6, -7, -7, -6, -7, -8, -8, -8, -9, -9, -9, -10, -9, -10, -10, -9, -10, -9, -9, -10, -11, -10, -10, -11, -10, -11, -11, -11, -12, -13, -13, -13, -13, -12, -12, -13, -13, -12, -12, -11, -12, -13

Offset: 1

Author

Wesley Ivan Hurt, Sep 16 2014

Keywords

• sign
• easy
• look

Comments

Alternating sums of mu(n), the Moebius function (A008683), from 1 to n.

Examples

			a(n) = mu(1) - mu(2) + mu(3) - mu(4) + ... + (-1)^(n+1) * mu(n).
		

Links

• Seiichi Manyama, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A008683 (moebius function).

Cf. A068773 (alternating sums of eulerphi(n)).

Cf. A068762 (alternating sums of sigma(n)).

Cf. A002321, A344432.

Programs

Maple

with(numtheory): A247418:=n->add(mobius(i)*(-1)^(i+1), i=1..n): seq(A247418(n), n=1..50);

Mathematica

Table[Sum[MoebiusMu[i] (-1)^(i + 1), {i, n}], {n, 50}]
Accumulate[Table[MoebiusMu[n](-1)^(n+1),{n,60}]] (* Harvey P. Dale, Oct 19 2018 *)

PARI

a(n) = sum(i=1, n, moebius(i)*(-1)^(i+1)); \\ Michel Marcus, Sep 18 2014

Formula

a(n) = Sum_{i=1..n} A008683(i)*(-1)^(i+1).