login
This site is supported by donations to The OEIS Foundation.

 

Logo

Annual Appeal: Today, Nov 11 2014, is the 4th anniversary of the launch of the new OEIS web site. 70,000 sequences have been added in these four years, all edited by volunteers. Please make a donation (tax deductible in the US) to help keep the OEIS running.

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A101035 Dirichlet inverse of the gcd-sum function (A018804). 4
1, -3, -5, 1, -9, 15, -13, 1, 4, 27, -21, -5, -25, 39, 45, 1, -33, -12, -37, -9, 65, 63, -45, -5, 16, 75, 4, -13, -57, -135, -61, 1, 105, 99, 117, 4, -73, 111, 125, -9, -81, -195, -85, -21, -36, 135, -93, -5, 36, -48, 165, -25, -105, -12, 189, -13, 185, 171, -117, 45, -121, 183, -52, 1, 225, -315, -133, -33, 225, -351, -141, 4 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

G. P. Michon, Multiplicative Functions.

FORMULA

Multiplicative function with a(p)=1-2p and a(p^e)=(p-1)^2 when e>1 [p prime].

Dirichlet g.f. zeta(s)/zeta^2(s-1). - R. J. Mathar, Apr 10 2011

a(n)=Sum{d|n} tau_{-2}(d)*d, where tau_{-2} is A007427. - Enrique Pérez Herrero, Jan 19 2013

EXAMPLE

a(4)=1, a(8)=1, a(16)=1, a(32)=1, etc. because of the multiplicative definition for powers of 2.

MATHEMATICA

DirichletInverse[f_][1] = 1/f[1]; DirichletInverse[f_][n_] := DirichletInverse[f][n] = -1/f[1]*Sum[ f[n/d]*DirichletInverse[f][d], {d, Most[ Divisors[n]]}]; GCDSum[n_] := Sum[ GCD[n, k], {k, 1, n}]; Table[ DirichletInverse[ GCDSum][n], {n, 1, 72}](* Jean-François Alcover, Dec 12 2011 *)

PROG

(Haskell)

a101035 n = product $ zipWith f (a027748_row n) (a124010_row n) where

   f p 1 = 1 - 2 * p

   f p e = (p - 1) ^ 2

-- Reinhard Zumkeller, Jul 16 2012

CROSSREFS

Cf. A018804, A055615, A046692, A023900, A007427, A053822, A053825, A053826.

Cf. A008683.

Sequence in context: A214229 A214728 A112752 * A204029 A026253 A138259

Adjacent sequences:  A101032 A101033 A101034 * A101036 A101037 A101038

KEYWORD

easy,nice,sign,mult

AUTHOR

Gerard P. Michon, Nov 27 2004

STATUS

approved

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

Content is available under The OEIS End-User License Agreement .

Last modified November 28 12:57 EST 2014. Contains 250359 sequences.