A245656 - OEIS

A245656

Characteristic function of arithmetic numbers, cf. A003601.

1, 0, 1, 0, 1, 1, 1, 0, 0, 0, 1, 0, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 0, 0, 1, 0, 1, 1, 1, 0, 1, 0, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 0, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 0, 1

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OFFSET

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..16384

Antti Karttunen, Data supplement: n, a(n) computed for n = 1..100000

Paul T. Bateman, Paul Erdős, Carl Pomerance, and E. G. Straus, The arithmetic mean of the divisors of an integer, in: Marvin I. Knopp (ed.), Analytic number theory, Proceedings of a Conference Held at Temple University, Philadelphia, May 12-15, 1980, Lecture Notes in Mathematics, Vol. 899, Springer-Verlag, 1981, pp. 197-220; alternative link.

Wikipedia, Arithmetic number.

Index entries for characteristic functions.

FORMULA

a(n) = A000007(A054025(n)).

a(A003601(n)) = 1; a(A049642(n)) = 0.

Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = 1 (Bateman et al., 1981) . - Amiram Eldar, Dec 28 2024

MATHEMATICA

a[n_] := Boole[IntegerQ[Mean[Divisors[n]]]];

Array[a, 105] (* Jean-François Alcover, Dec 02 2021 *)

PROG

(Haskell)

a245656 = (0 ^) . a054025 :: (Integral a, Integral t) => a -> t