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A353557
a(n) = 1 if n is an odd number with an even number of prime factors (counted with multiplicity), otherwise 0.
30
1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1
OFFSET
1
FORMULA
a(n) = A000035(n) * A065043(n).
a(n) = A000035(n) - A353558(n).
a(n) = A065043(n) - A353555(n).
For n >= 1, A353480(n) <= a(n) <= A353374(n).
For n >= 1, a(n) = A059841(A327858(n)). [See comments in the latter sequence]
a(n) = [A166698(n) > 0], where [ ] is the Iverson bracket. - Antti Karttunen, Dec 30 2022
a(n) = A059841(A095112(n)). [From Sequence Machine] - Antti Karttunen, Nov 22 2023
a(n) = A353495(n) + A360109(n). - Antti Karttunen, Feb 05 2024
PROG
(PARI) A353557(n) = ((n%2)&&(!(bigomega(n)%2)));
(Python)
from functools import reduce
from operator import ixor
from sympy import factorint
def A353557(n): return 1&n&(reduce(ixor, factorint(n).values(), 0)^1) # Chai Wah Wu, Dec 21 2022
CROSSREFS
Characteristic function of A046337.
Cf. A000035, A001222, A059841, A065043, A095112, A166698, A327858, A353374, A353480, A353555, A353556, A353558, A358777 (Dirichlet inverse), A369257 (inverse Möbius transform).
Cf. also A353495, A360109, A369001.
Sequence in context: A287457 A358777 A359595 * A324917 A369974 A369975
KEYWORD
nonn
AUTHOR
Antti Karttunen, May 01 2022
STATUS
approved