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%I #13 Sep 03 2015 10:53:33
%S 35,77,143,165,187,209,231,247,273,299,357,391,399,437,493,527,561,
%T 589,598,713,715,943,989,1015,1073,1189,1247,1295,1333,1537,1547,1705,
%U 1729,1739,1829,1886,1927,1961,2015,2021,2257,2279,2387,2397,2419,2451,2479,2501
%N Quasi-Carmichael numbers to exactly one base.
%C See A259238 for the corresponding bases.
%H Tim Johannes Ohrtmann, <a href="/A257751/b257751.txt">Table of n, a(n) for n = 1..14688</a>
%e a(1) = 35 because this is the first squarefree composite number n such that exactly one nonzero integer b exists such that for every prime factor p of n, 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); k=0; for(b=-(f[1, 1]-1), n, c=0; for(i=1, #f[, 1], if((n+b)%(f[i, 1]+b)>0, c++)); if(c==0, if(!b==0, k++))); if(k==1, print1(n, ", ")))))
%Y Cf. A257750 (every number of bases).
%Y Cf. A257752, A257753, A257754, A257755, A257756, A257757, A258842 (2 to 8 bases).
%Y Cf. A257758 (first occurrences).
%K nonn
%O 1,1
%A _Tim Johannes Ohrtmann_, May 07 2015
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