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 A257757 #37 Sep 28 2015 07:51:57 %S A257757 777923,1030189,1060459,4903309,5493247,5659637,6431071,6673087, %T A257757 6778969,9790577,11390429,11860969,12053263,12390319,12602059, %U A257757 21215011,21842629,22991989,24005239,39339667,39929437,40080661,40761169,42314449,50979479,51876007,54345943 %N A257757 Quasi-Carmichael numbers to exactly seven bases. %C A257757 All known terms have only two prime factors, one slightly larger than the other. %C A257757 a(435) = 7523021437 = 1597 * 1933 * 2437 is the first term which has more than two prime factors. - _Hiroaki Yamanouchi_, Sep 28 2015 %C A257757 a(5586) > 10^12. - _Hiroaki Yamanouchi_, Sep 28 2015 %H A257757 Hiroaki Yamanouchi, <a href="/A257757/b257757.txt">Table of n, a(n) for n = 1..5885</a> %e A257757 a(1) = 777923 because this is the first squarefree composite number n such that exactly seven integers b except 0 exist such that for every prime factor p of n, p+b divides n+b (-879, -878, -875, -872, -867, -863, -839): 777923=881*883 and 2, 4 both divide 777044 and 3, 5 both divide 777045 and 6, 8 both divide 777048 and 9, 11 both divide 777051 and 14, 16 both divide 777056 and 18, 20 both divide 777060 and 42, 44 both divide 777084. %o A257757 (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==7, print1(n, ", "))))) %Y A257757 Cf. A257750 (every number of bases). %Y A257757 Cf. A257751, A257752, A257753, A257754, A257755, A257756, A258842 (1 to 6 and 8 bases). %Y A257757 Cf. A257758 (first occurrences). %K A257757 nonn %O A257757 1,1 %A A257757 _Tim Johannes Ohrtmann_, May 12 2015 %E A257757 a(16)-a(27) from _Hiroaki Yamanouchi_, Sep 26 2015