The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A055615 a(n) = n*moebius(n) (cf. A008683). 54
 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 G.f. A(x) satisfies: A(x) = x - Sum_{k>=2} k*A(x^k). - Ilya Gutkovskiy, May 11 2019 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 A332845 A190621 Adjacent sequences:  A055612 A055613 A055614 * A055616 A055617 A055618 KEYWORD sign,easy,nice,mult AUTHOR Michael Somos, Jun 04 2000 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified August 13 02:09 EDT 2020. Contains 336441 sequences. (Running on oeis4.)