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

1,1

Links

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

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, 1<d<n} d * A055615(n/d). [As A000027 and A055615 are Dirichlet inverses of each other]

(End)

Example

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

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 *)

Prog

(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

Crossrefs

Cf. A000027, A008683, A007423, A055615.

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

Sequence in context: A071390 A354350 A323884 * A324641 A365804 A349359

Adjacent sequences: A061666 A061667 A061668 * A061670 A061671 A061672

Keyword

easy,nonn

Author

Jason Earls, Jun 16 2001

Extensions

More terms from Dean Hickerson, Jul 24 2001

Status

approved