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!)
 A166234 The inverse of the constant 1 function under the exponential convolution (also called the exponential Möbius 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 Xiaodong Cao and Wenguang Zahi, Some arithmetic functions involving exponential divisors, Journal of Integer Sequences, Vol. 13 (2010), Article 10.3.7. Andrew V. Lelechenko, Exponential and infinitary divisors, Ukrainian Mathematical Journal, Vol. 68, No. 8 (2017), pp. 1222-1237; arXiv preprint, arXiv:1405.7597 [math.NT], 2014, function mu^(E)(n). M. V. Subbarao, On some arithmetic convolutions, in: A. A. Gioia and D. L. Goldsmith (eds.), The Theory of Arithmetic Functions, Lecture Notes in Mathematics No. 251, Springer, 1972, pp. 247-271; alternative link. László Tóth, On certain arithmetic functions involving exponential divisors, Annales Univ. Sci. Budapest., Sect. Comp., Vol. 24 (2004), pp. 285-296; arXiv preprint, arXiv:math/0610274 [math.NT], 2006-2009. László Tóth, On certain arithmetic functions involving exponential divisors, II, Annales Univ. Sci. Budapest., Sect. Comp., Vol. 27 (2007), pp. 155-166; arXiv preprint, arXiv:0708.3557 [math.NT], 2007-2009. FORMULA Multiplicative, a(p^e) = mu(e) for any prime power p^e (e>=1), where mu is the Möbius function A008683. a(A130897(n)) = 0; a(A209061(n)) <> 0. - Reinhard Zumkeller, Mar 13 2012 Asymptotic mean: lim_{n->oo} (1/n) * Sum_{k=1..n} a(k) = Product_{p prime} (1 + Sum_{k>=2} (mu(k) - mu(k-1))/p^k) = 0.3609447238... (Tóth, 2007). - Amiram Eldar, Nov 08 2020 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. A008683, A049419, A051377, A124010, A209802 (partial sums). Sequence in context: A307430 A053865 A189022 * 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
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified July 25 03:53 EDT 2021. Contains 346283 sequences. (Running on oeis4.)