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A370598
Characteristic function of exponentially squarefree numbers (A209061).
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, 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
OFFSET
1
LINKS
Jean-Marie De Koninck and William Verreault, On the tower factorization of integers, arXiv:2308.09149 [math.NT], 2023. See page 2.
FORMULA
Multiplicative with a(p^e) = mu(e)^2, where mu is the Möbius function (A008683).
a(n) = 1 if and only if n is in A209061.
a(n) = 0 if and only if n is in A130897.
a(n) = abs(A166234(n)).
Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = A262276.
MATHEMATICA
f[p_, e_] := MoebiusMu[e]^2; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100]
PROG
(PARI) a(n) = vecprod(apply(x -> moebius(x)^2, factor(n)[, 2]));
CROSSREFS
KEYWORD
nonn,easy,mult
AUTHOR
Amiram Eldar, Feb 23 2024
STATUS
approved