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%I
%S 60491,61937,65311,76151,116843,127723,159197,164009,168821,194417,
%T 272483,284987,329467,364087,369857,370817,385241,389327,395497,
%U 407837,423701,431393,465043,509461,613927,837209,853607,881717,999919,1041541,1117213,1279903,1294819
%N Quasi-Carmichael numbers to exactly four bases.
%H Tim Johannes Ohrtmann, <a href="/A257754/b257754.txt">Table of n, a(n) for n = 1..145</a>
%e a(1) = 60491 because this is the first squarefree composite number n such that exactly four integers b except 0 exist such that for every prime factor p of n, p+b divides n+b (-239, -236, -231, -191): 60491=241*251 and 2, 12 both divide 60252 and 5, 15 both divide 60255 and 10, 20 both divide 60260 and 50, 60 both divide 60300.
%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==4, print1(n, ", ")))))
%Y Cf. A257750 (every number of bases).
%Y Cf. A257751, A257752, A257753, A257755, A257756, A257757, A258842 (1, 2, 3, 5, 6, 7 and 8 bases).
%Y Cf. A257758 (first occurrences).
%K nonn
%O 1,1
%A _Tim Johannes Ohrtmann_, May 12 2015
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