|
%I #14 Sep 16 2015 00:47:05
%S 1517,1763,4331,4453,5183,5767,9797,10573,12317,14351,16637,34571,
%T 35657,38021,38191,38407,40723,41989,50429,50851,57599,67721,70151,
%U 75067,79523,87953,111547,117613,150463,159559,167137,173633,181451,190087,191819,197881,205193
%N Quasi-Carmichael numbers to exactly three bases.
%H Tim Johannes Ohrtmann, <a href="/A257753/b257753.txt">Table of n, a(n) for n = 1..403</a>
%e a(1) = 1517 because this is the first squarefree composite number n such that exactly three integers b except 0 exist such that for every prime factor p of n, p+b divides n+b (-35, -32, -29): 1517=37*41 and 2, 6 both divide 1482 and 5, 9 both divide 1485 and 8, 12 divide 1488.
%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==3, print1(n, ", ")))))
%Y Cf. A257750 (every number of bases).
%Y Cf. A257751, A257752, A257754, A257755, A257756, A257757, A258842 (1, 2, 4, 5, 6, 7 and 8 bases).
%Y Cf. A257758 (first occurrences).
%K nonn
%O 1,1
%A _Tim Johannes Ohrtmann_, May 07 2015
|
