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%I #16 Jun 17 2022 14:52:52
%S 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,
%T 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,
%U 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
%N a(n) = 1 if A345993(n) < A345992(n), otherwise 0.
%H Antti Karttunen, <a href="/A354989/b354989.txt">Table of n, a(n) for n = 1..100000</a>
%H <a href="/index/Ch#char_fns">Index entries for characteristic functions</a>
%F a(n) = [A354988(n) < 0], where [ ] is the Iverson bracket.
%t 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 *)
%o (PARI) A354989(n) = for(m=1, oo, if((m*(m+1))%n==0, return(gcd(n, 1+m)<gcd(n, m))));
%o (Python 3.8+)
%o from math import gcd, prod
%o from itertools import combinations
%o from sympy import factorint
%o from sympy.ntheory.modular import crt
%o def A354989(n):
%o if n == 1:
%o return 0
%o plist = tuple(p**q for p, q in factorint(n).items())
%o 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
%Y Characteristic function of A345995.
%Y Cf. A345992, A345993, A354988.
%K nonn
%O 1
%A _Antti Karttunen_, Jun 16 2022
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