A361023 - OEIS

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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 (list; graph; refs; listen; history; text; internal format)

	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`

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Last modified August 29 17:19 EDT 2024. Contains 375518 sequences. (Running on oeis4.)