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%I #9 Nov 23 2020 06:11:26
%S 1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,4,17,18,19,20,21,22,23,24,25,26,
%T 27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,12,49,
%U 50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68
%N The largest e-squarefree e-divisor of n.
%C An exponential squarefree exponential divisor (e-squarefree e-divisor) d = Product p_i^f_i of n = Product p_i^e_i has f_i | e_i and f_i is squarefree for all i.
%C The largest of the A278908(n) e-squarefree e-divisors of n.
%C a(n) = n if and only if n is an exponentially squarefree number (A209061).
%H Amiram Eldar, <a href="/A338782/b338782.txt">Table of n, a(n) for n = 1..10000</a>
%H László Tóth, <a href="http://ac.inf.elte.hu/Vol_027_2007/155.pdf">On certain arithmetic functions involving exponential divisors, II</a>, Annales Univ. Sci. Budapest., Sect. Comp., Vol. 27 (2007), pp. 155-166, <a href="https://arxiv.org/abs/0708.3557">arXiv preprint</a>, arXiv:0708.3557 [math.NT], 2007-2009.
%F Multiplicative with a(p^e) = p^rad(e), where rad(k) is the largest squarefree number dividing k (A007947).
%F Sum_{n<=x} a(n) = (1/2) * c * x^2, where c = Product_{p prime} Sum{k>=4} (p^rad(k) - p^(1+rad(k-1)))/p^(2*k) = 0.9646498658... (Tóth, 2007).
%t rad[n_] := Times @@ (First@# & /@ FactorInteger[n]); f[p_, e_] := p^rad[e]; a[1]=1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100]
%Y Cf. A005117, A007947, A209061, A278908.
%K nonn,mult
%O 1,2
%A _Amiram Eldar_, Nov 08 2020
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