A370598 Characteristic function of exponentially squarefree numbers (A209061).

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

Amiram Eldar, Table of n, a(n) for n = 1..10000

Jean-Marie De Koninck and William Verreault, On the tower factorization of integers, arXiv:2308.09149 [math.NT], 2023. See page 2.

Index entries for sequences related to characteristic functions.

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

Cf. A008683, A130897, A209061, A262276.

Sequence in context: A307430 A053865 A189022 * A166234 A074481 A015420

Adjacent sequences: A370595 A370596 A370597 * A370599 A370600 A370601

Keyword

nonn,easy,mult

Author

Amiram Eldar, Feb 23 2024

Status

approved