The On-Line Encyclopedia of Integer Sequences (OEIS)

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A370598

Characteristic function of exponentially squarefree numbers (A209061).
(history; published version)

#9 by OEIS Server at Fri Feb 23 08:29:51 EST 2024

LINKS

Amiram Eldar, <a href="/A370598/b370598_1.txt">Table of n, a(n) for n = 1..10000</a>

#8 by Michael De Vlieger at Fri Feb 23 08:29:51 EST 2024

STATUS

reviewed

approved

Discussion

Fri Feb 23

08:29

OEIS Server: Installed first b-file as b370598.txt.

#7 by Vaclav Kotesovec at Fri Feb 23 08:28:18 EST 2024

STATUS

proposed

reviewed

#6 by Amiram Eldar at Fri Feb 23 03:16:09 EST 2024

STATUS

editing

proposed

#5 by Amiram Eldar at Fri Feb 23 03:15:13 EST 2024

LINKS

Jean-Marie De Koninck and William Verreault, <a href="https://arxiv.org/abs/2308.09149">On the tower factorization of integers</a>, arXiv:2308.09149 [math.NT], 2023. See page 2.

#4 by Amiram Eldar at Fri Feb 23 03:13:44 EST 2024

LINKS

<a href="/index/Ch#char_fns">Index entries for sequences related to characteristic functions</a>.

#3 by Amiram Eldar at Fri Feb 23 03:02:36 EST 2024

LINKS

Amiram Eldar, <a href="/A370598/b370598_1.txt">Table of n, a(n) for n = 1..10000</a>

#2 by Amiram Eldar at Fri Feb 23 03:01:32 EST 2024

NAME

allocated for Amiram EldarCharacteristic function of exponentially squarefree numbers (A209061).

DATA

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, <a href="https://arxiv.org/abs/2308.09149">On the tower factorization of integers</a>, arXiv:2308.09149 [math.NT], 2023.

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.

KEYWORD

allocated

nonn,easy,mult

AUTHOR

Amiram Eldar, Feb 23 2024

STATUS

approved

editing

#1 by Amiram Eldar at Fri Feb 23 03:01:32 EST 2024

NAME

allocated for Amiram Eldar

KEYWORD

allocated

STATUS

approved