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%I #10 Sep 21 2015 20:38:06
%S 35,77,143,187,209,221,247,299,323,391,437,493,527,561,589,713,899,
%T 943,989,1073,1105,1147,1189,1247,1271,1295,1333,1517,1537,1591,1595,
%U 1705,1729,1739,1763,1829,1927,1961,2021,2093,2257,2279,2419,2465,2479,2501,2623
%N Quasi-Carmichael numbers to at least one negative base.
%H Tim Johannes Ohrtmann, <a href="/A259282/b259282.txt">Table of n, a(n) for n = 1..100000</a>
%e a(1) = 35 because this is the first squarefree composite number n such that at least one negative integer b exists such that for every prime factor p of n applies that p+b divides n+b (-3): 35=5*7 and 2, 4 both divide 32.
%o (PARI) for(n=2, 1000000, if(!isprime(n), if(issquarefree(n), f=factor(n); b=-f[1, 1]; until(c==0 || b==-1, b++; c=0; for(i=1, #f[, 1], if((n+b)%(f[i, 1]+b)>0, c++)); if(c==0, print1(n, ", "))))))
%Y Cf. A257750, A257759, A259283.
%K nonn
%O 1,1
%A _Tim Johannes Ohrtmann_, Jun 23 2015
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