A354920 a(n) = A182665(n) mod 2, where A182665(n) is the greatest x < n such that n divides x*(x-1).

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

Offset

1

Links

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

Index entries for characteristic functions

Formula

a(n) = A000035(A182665(n)).

a(n) = A000035(n) XOR A354918(n), where XOR is bitwise-XOR, A003987.

Prog

(PARI) A354920(n) = forstep(x=n-1, 0, -1, if(!((x*(x-1))%n), return(x%2)));
(Python 3.8+)
from itertools import combinations
from math import prod
from sympy import factorint
from sympy.ntheory.modular import crt
def A354920(n):
    if n == 1:
        return 0
    plist = tuple(p**q for p, q in factorint(n).items())
    return 1 if len(plist) == 1 else (n-int(min(min(crt((m, n//m), (0, -1))[0], crt((n//m, m), (0, -1))[0]) for m in (prod(d) for l in range(1, len(plist)//2+1) for d in combinations(plist, l))))) & 1 # Chai Wah Wu, Jun 12 2022

Crossrefs

Parity of A182665. Characteristic function of A354921.

Cf. A000035, A003987, A354918.

Sequence in context: A268411 A069513 A092248 * A106743 A284944 A284674

Adjacent sequences: A354917 A354918 A354919 * A354921 A354922 A354923

Keyword

nonn

Author

Antti Karttunen, Jun 12 2022

Status

approved