A354989 a(n) = 1 if A345993(n) < A345992(n), otherwise 0.

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

Offset

1

Links

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

Index entries for characteristic functions

Formula

a(n) = [A354988(n) < 0], where [ ] is the Iverson bracket.

Mathematica

a[n_] := Module[{m = 1}, While[! Divisible[m*(m + 1), n], m++]; If[GCD[n, m + 1] < GCD[n, m], 1, 0]]; Array[a, 100] (* Amiram Eldar, Jun 16 2022 *)

Prog

(PARI) A354989(n) = for(m=1, oo, if((m*(m+1))%n==0, return(gcd(n, 1+m)<gcd(n, m))));
(Python 3.8+)
from math import gcd, prod
from itertools import combinations
from sympy import factorint
from sympy.ntheory.modular import crt
def A354989(n):
    if n == 1:
        return 0
    plist = tuple(p**q for p, q in factorint(n).items())
    return 0 if len(plist) == 1 else int(gcd(n, s:=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))))) > gcd(n, s+1)) # Chai Wah Wu, Jun 16 2022

Crossrefs

Characteristic function of A345995.

Cf. A345992, A345993, A354988.

Sequence in context: A327932 A373979 A359546 * A277161 A353481 A353677

Adjacent sequences: A354986 A354987 A354988 * A354990 A354991 A354992

Keyword

nonn

Author

Antti Karttunen, Jun 16 2022

Status

approved