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%I #22 Jun 13 2022 02:27:45
%S 1,1,0,1,0,0,0,1,0,0,0,1,0,0,1,1,0,0,0,0,0,0,0,0,0,0,0,1,0,1,0,1,1,0,
%T 0,0,0,0,0,1,0,0,0,1,1,0,0,1,0,0,1,0,0,0,0,1,0,0,0,1,0,0,1,1,1,1,0,0,
%U 1,0,0,0,0,0,0,1,1,0,0,1,0,0,0,0,0,0,1,0,0,1,1,1,0,0,1,0,0,0,0,0,0,1,0,1,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,1,0
%N a(n) = A344005(n) mod 2, where A344005(n) is the smallest positive m such that n divides the oblong number m*(m+1).
%H Antti Karttunen, <a href="/A354918/b354918.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) = A000035(A344005(n)).
%F a(n) = A000035(n) XOR A354920(n), where XOR is bitwise-XOR, A003987.
%o (PARI) A354918(n) = for(m=1, oo, if((m*(m+1))%n==0, return(m%2)));
%o (Python 3.8+)
%o from itertools import combinations
%o from math import prod
%o from sympy import factorint
%o from sympy.ntheory.modular import crt
%o def A354918(n):
%o if n == 1:
%o return 1
%o plist = tuple(p**q for p, q in factorint(n).items())
%o return (n-1 if len(plist) == 1 else 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
%Y Characteristic function of A354919. Parity of A344005.
%Y Cf. A000035, A002378, A003987, A343999 (even bisection), A354920.
%K nonn
%O 1
%A _Antti Karttunen_, Jun 12 2022