This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A257756 #15 Sep 21 2015 20:37:26 %S A257756 189029,404471,424663,2595221,4140901,4197377,4347209,4528159,4566193, %T A257756 4631023,4708819,4864411,5175589,5311729,6380651,6400819,6426029, %U A257756 7117783,8173877,8915971,10080589,10460869,10671173,11094661,11538313 %N A257756 Quasi-Carmichael numbers to exactly six bases. %e A257756 a(1) = 189029 because this is the first squarefree composite number n such that exactly six integers b except 0 exist such that for every prime factor p of n, p+b divides n+b (-419, -414, -407, -389, -365, -309): 189029=421*449 and 2, 30 both divide 188610 and 7, 35 both divide 188615 and 14, 42 both divide 188622 and 32, 60 both divide 188640 and 56, 84 both divide 188664 and 112, 140 both divide 188720. %o A257756 (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==6, print1(n, ", "))))) %Y A257756 Cf. A257750 (every number of bases). %Y A257756 Cf. A257751, A257752, A257753, A257754, A257755, A257757, A258842 (1, 2, 3, 4, 5, 7 and 8 bases). %Y A257756 Cf. A257758 (first occurrences). %K A257756 nonn %O A257756 1,1 %A A257756 _Tim Johannes Ohrtmann_, May 12 2015