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 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

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