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A324903
a(n) = 1 if A007814(sigma(n)) > A007814(n), 0 otherwise. Here A007814(n) gives the 2-adic valuation of n.
8
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.
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
KEYWORD
nonn
AUTHOR
Antti Karttunen, Mar 28 2019
STATUS
approved