A324903 a(n) = 1 if A007814(sigma(n)) > A007814(n), 0 otherwise. Here A007814(n) gives the 2-adic valuation of n.

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

Offset

1

Comments

Characteristic function of A216782.

Difference between 2-adic valuations of (2*n OR sigma(n)) and (n OR (sigma(n)-n)), where OR is bitwise-OR, A003986.

Links

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

Jon Maiga, Computer-generated formulas for A324903, Sequence Machine

Index entries for characteristic functions

Index entries for sequences related to sigma(n)

Formula

a(n) = A324904(n) - A324902(n).

a(n) = A324883(A005940(1+n)).

From Antti Karttunen, Mar 20 2023: (Start)

These are also listed by Maiga's Sequence Machine:

a(n) = A059841(A098987(n)).

a(n) = A361023(n) - A361024(n) = A361023(2*n).

a(n) = A059841(A017665(n)) = A059841(sigma(n)/gcd(n, sigma(n))).

a(n) = A324902(2*n) - A324902(n).

a(n) = A000035(A249670(n)-A017666(n)) = A000035(A249670(n)+A017666(n)).

a(n) = -1 + A325636(n)/A009194(n).

a(n) = A169813(A325635(n)/A325634(n)).

(End)

Prog

(PARI) A324903(n) = (valuation(n, 2)<valuation(sigma(n), 2));
(PARI)
A318456(n) = bitor(n, sigma(n)-n);
A318466(n) = bitor(2*n, sigma(n));
A324902(n) = valuation(A318456(n), 2);
A324904(n) = valuation(A318466(n), 2);
A324903(n) = (A324904(n)-A324902(n));
(Python)
from sympy import divisor_sigma
def A324903(n): return int((~(m:=int(divisor_sigma(n)))&m-1).bit_length()>(~n&n-1).bit_length()) # Chai Wah Wu, Jul 11 2022

Crossrefs

Cf. A000035, A000203, A003986, A005940, A007814, A009194, A017665, A059841, A098987, A216782, A243473, A249670, A286357, A318456, A318466, A324883, A324902, A324904, A325636, A361023, A361024.

Sequence in context: A242018 A324682 A288132 * A011656 A295309 A353670

Adjacent sequences: A324900 A324901 A324902 * A324904 A324905 A324906

Keyword

nonn

Author

Antti Karttunen, Mar 28 2019

Status

approved