%I #9 Dec 30 2023 09:33:32

%S 2,2,2,2,3,2,2,2,2,2,2,2,4,2,2,2,3,2,2,2,2,2,2,2,4,2,4,2,2,3,3,2,2,2,

%T 2,2,2,2,4,2,4,3,2,2,2,2,2,2,2,2,2,2,2,2,6,2,2,2,2,2,2,2,3,2,2,2,2,2,

%U 2,3,4,2,2,2,4,4,2,4,2,2,3,2,4,2,2,4,2,2,2,2,3,2,2,2,2,2,2,4,4,2,2,2,2,2,3,2,2,2,2,2,4,2,2,2,2,2,4,3

%N The number of exponential divisors of the nonsquarefree numbers.

%C The terms of A049419 that are larger than 1, since A049419(k) = 1 if and only if k is squarefree (A005117).

%H Amiram Eldar, <a href="/A368541/b368541.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) = A049419(A013929(n)).

%F Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = (A327837 - A059956)/A229099 = 2.53623753427906735929... .

%t f[p_, e_] := DivisorSigma[0, e]; s[n_] := Times @@ f @@@ FactorInteger[n]; Select[Array[s, 200], # > 1 &]

%o (PARI) lista(kmax) = {my(p, f); for(k = 1, kmax, f = factor(k); p = prod(i=1, #f~, numdiv(f[i, 2])); if(p > 1, print1(p, ", ")));}

%Y Cf. A005117, A013929, A049419.

%Y Cf. A084936, A174961, A275699, A368038, A368039, A368040.

%Y Cf. A013661, A059956, A229099, A327837.

%K nonn

%O 1,1

%A _Amiram Eldar_, Dec 29 2023