A361023 a(n) = 1 if A007814(sigma(n)) >= A007814(n), otherwise 0, where A007814(n) gives the 2-adic valuation of n.

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

Offset

1

Comments

Parity of A017666(n), the denominator of sigma(n)/n (the abundancy index of n).

Links

Antti Karttunen, Table of n, a(n) for n = 1..100000

Index entries for characteristic functions

Index entries for sequences related to sigma(n)

Formula

a(n) = [A336937(n) >= A007814(n)] = [A361025(n) > 0], where [ ] is the Iverson bracket.

a(n) = A324903(n) + A361024(n).

a(n) = A000035(A017666(n)) = A000035(n / gcd(sigma(n), n)).

Mathematica

a[n_] := Mod[Denominator[DivisorSigma[-1, n]], 2]; Array[a, 100] (* Amiram Eldar, Mar 03 2023 *)

Prog

(PARI) A361023(n) = (valuation(sigma(n), 2)>=valuation(n, 2));

Crossrefs

Cf. A000035, A000203, A007814, A017666, A319338, A319346, A324903, A336937, A361024, A361025.

Cf. A216781 (positions of 0's).

Sequence in context: A283966 A054354 A156728 * A267442 A267129 A267848

Adjacent sequences: A361020 A361021 A361022 * A361024 A361025 A361026

Keyword

nonn

Author

Antti Karttunen, Mar 03 2023

Status

approved