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A368541
The number of exponential divisors of the nonsquarefree numbers.
2
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, 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, 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
OFFSET
1,1
COMMENTS
The terms of A049419 that are larger than 1, since A049419(k) = 1 if and only if k is squarefree (A005117).
LINKS
FORMULA
a(n) = A049419(A013929(n)).
Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = (A327837 - A059956)/A229099 = 2.53623753427906735929... .
MATHEMATICA
f[p_, e_] := DivisorSigma[0, e]; s[n_] := Times @@ f @@@ FactorInteger[n]; Select[Array[s, 200], # > 1 &]
PROG
(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, ", "))); }
KEYWORD
nonn
AUTHOR
Amiram Eldar, Dec 29 2023
STATUS
approved