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.
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
KEYWORD
mult,sign
AUTHOR
Laszlo Toth, Oct 09 2009
STATUS
approved