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A055615 n*moebius(n) (cf. A008683). 31
1, -2, -3, 0, -5, 6, -7, 0, 0, 10, -11, 0, -13, 14, 15, 0, -17, 0, -19, 0, 21, 22, -23, 0, 0, 26, 0, 0, -29, -30, -31, 0, 33, 34, 35, 0, -37, 38, 39, 0, -41, -42, -43, 0, 0, 46, -47, 0, 0, 0, 51, 0, -53, 0, 55, 0, 57, 58, -59, 0, -61, 62, 0, 0, 65, -66, -67, 0, 69, -70, -71, 0 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Dirichlet inverse of n.

Absolute values give n if n is squarefree, otherwise 0.

Equals row sums of triangle A127507, A127475. - Gary W. Adamson, May 01 2010

Negative of the Moebius number of the dihedral group of order 2n. - Eric M. Schmidt, Jul 28 2013

LINKS

T. D. Noe, Table of n, a(n) for n=1..1000

Mats Granvik, Primes approximated by eigenvalues

Mats Granvik, Mobius function times n approximated by eigenvalues

FORMULA

Dirichlet g.f.: 1/zeta(s-1).

Multiplicative with a(p^e) = -p*0^(e-1), e>0 and p prime. - Reinhard Zumkeller, Jul 17 2003

Conjectures: lim b->1+ Sum n=1..inf a(n)*b^(-n) = -12 and lim b->1- Sum n=1..inf a(n)*b^n = -12 (+ indicates that b decreases to 1, - indicates it increases to 1), both considering that zeta(-1) = -1/12 and calculations (more generally mu(n)*n^s is Abel summable to zeta(-s)). - Gerald McGarvey, Sep 26 2004

Dirichlet generating function for the absolute value: zeta(s-1)/zeta(2s-2). - Franklin T. Adams-Watters, Sep 11 2005

EXAMPLE

G.f. = x - 2*x^2 - 3*x^3 - 5*x^5 + 6*x^6 - 7*x^7 + 10*x^10 - 11*x^11 - 13*x^13 + ...

MAPLE

with(numtheory): A055615:=n->n*mobius(n): seq(A055615(n), n=1..100); # Wesley Ivan Hurt, Nov 18 2014

MATHEMATICA

Table[n MoebiusMu[n], {n, 80}] (* Harvey P. Dale, May 26 2011 *)

PROG

(PARI) {a(n) = if( n<1, 0, n * moebius(n))};

(PARI) {a(n) = if( n<1, 0, direuler(p=2, n, 1 - p*X)[n]))};

(MAGMA) [n*MoebiusMu(n): n in [1..80]]; // Vincenzo Librandi, Nov 19 2014

(Haskell)

a055615 n = a008683 n * n  -- Reinhard Zumkeller, Sep 04 2015

CROSSREFS

Cf. A000027. Moebius transform of A023900.

Cf. A008683, A062004.

Cf. A127475, A127507.

Cf. A068340 (partial sums), A261869 (first differences), A261890 (second differences).

Sequence in context: A248092 A145105 A140700 * A243059 A190621 A049268

Adjacent sequences:  A055612 A055613 A055614 * A055616 A055617 A055618

KEYWORD

sign,easy,nice,mult

AUTHOR

Michael Somos, Jun 04 2000

STATUS

approved

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Last modified June 23 05:55 EDT 2017. Contains 288635 sequences.