A061669 a(n) = n*(mu(n) + 1), where mu(n) is the Moebius function A008683.

2, 0, 0, 4, 0, 12, 0, 8, 9, 20, 0, 12, 0, 28, 30, 16, 0, 18, 0, 20, 42, 44, 0, 24, 25, 52, 27, 28, 0, 0, 0, 32, 66, 68, 70, 36, 0, 76, 78, 40, 0, 0, 0, 44, 45, 92, 0, 48, 49, 50, 102, 52, 0, 54, 110, 56, 114, 116, 0, 60, 0, 124, 63, 64, 130, 0, 0, 68, 138, 0, 0, 72, 0, 148, 75

Offset: 1

Author

Jason Earls, Jun 16 2001

Keywords

• easy
• nonn

Examples

			a(5) = (5 * -1) + 5 = 0 because mu(5)= -1.
		

Links

• Antti Karttunen, Table of n, a(n) for n = 1..20000 (first 1000 terms from Harry J. Smith)

Crossrefs

Cf. A000027, A008683, A007423, A055615.

Cf. A030059 (positions of 0's), A053850 (positions of odd terms).

Programs

Maple

with(numtheory): seq(n*(mobius(n)+1),n=1..80); # Muniru A Asiru, Jul 01 2018

Mathematica

Array[# (MoebiusMu[#] + 1) &, 75] (* Michael De Vlieger, Jul 01 2018 *)

PARI

for(n=1,20,print(n*moebius(n)+n))

PARI

{ for (n=1, 1000, write("b061669.txt", n, " ", n*moebius(n) + n) ) } \\ Harry J. Smith, Jul 26 2009

PARI

A061669(n) = (n*(1+moebius(n))); \\ Antti Karttunen, May 03 2022

Formula

From Antti Karttunen, May 03 2022: (Start)

a(n) = n * A007423(n) = n*(1+A008683(n)) = n + A055615(n).

a(1) = 2, and for n > 1, a(n) = -Sum_{d|n, 1A055615(n/d). [As A000027 and A055615 are Dirichlet inverses of each other]

(End)

Extensions

More terms from Dean Hickerson, Jul 24 2001