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

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A166234 The inverse of the constant 1 function under the exponential convolution (also called the exponential Moebius function). 6
1, 1, 1, -1, 1, 1, 1, -1, -1, 1, 1, -1, 1, 1, 1, 0, 1, -1, 1, -1, 1, 1, 1, -1, -1, 1, -1, -1, 1, 1, 1, -1, 1, 1, 1, 1, 1, 1, 1, -1, 1, 1, 1, -1, -1, 1, 1, 0, -1, -1, 1, -1, 1, -1, 1, -1, 1, 1, 1, -1, 1, 1, -1, 1, 1, 1, 1, -1, 1, 1, 1, 1, 1, 1, -1, -1, 1, 1, 1, 0, 0, 1, 1, -1, 1, 1, 1, -1, 1, -1, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

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

X. Cao, W. Zahi, Some arithmetic functions involving exponential divisors, JIS 13 (2010) # 10.3.7.

A. V. Lelechenko, Exponential and infinitary divisors, arXiv:1405.7597 [math.NT], 2014, function mu^(E)(n).

M. V. Subbarao, On some arithmetic convolutions, in The Theory of Arithmetic Functions, Lecture Notes in Mathematics No. 251, 247-271, Springer, 1972, DOI.

L. Toth, On certain arithmetic functions involving exponential divisors, II. , arXiv:math/0610274 [math.NT], 2006-2009; Annales Univ. Sci. Budapest., Sect. Comp., 27 (2007), 155-166.

FORMULA

Multiplicative, a(p^e) = mu(e) for any prime power p^e (e>=1), where mu is the Moebius function A008683.

a(A130897(n)) = 0; a(A209061(n)) <> 0. - Reinhard Zumkeller, Mar 13 2012

MAPLE

A166234 := proc(n)

    local a, p;

    a := 1;

    if n =1 then

        ;

    else

        for p in ifactors(n)[2] do

                    a := a*numtheory[mobius](op(2, p)) ;

        end do:

    end if;

    a ;

end proc:# R. J. Mathar, Nov 30 2016

MATHEMATICA

a[n_] := Times @@ MoebiusMu /@ FactorInteger[n][[All, 2]];

Array[a, 100] (* Jean-François Alcover, Nov 16 2017 *)

PROG

(Haskell)

a166234 = product . map (a008683 . fromIntegral) . a124010_row

-- Reinhard Zumkeller, Mar 13 2012

(PARI) a(n)=factorback(apply(moebius, factor(n)[, 2])) \\ Charles R Greathouse IV, Sep 02 2015

CROSSREFS

Cf. A049419, A051377, A124010, A209802 (partial sums).

Sequence in context: A167850 A167851 A053865 * A074481 A015420 A015522

Adjacent sequences:  A166231 A166232 A166233 * A166235 A166236 A166237

KEYWORD

mult,sign

AUTHOR

Laszlo Toth, Oct 09 2009

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 | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified November 16 15:42 EST 2018. Contains 317274 sequences. (Running on oeis4.)