A257752 Quasi-Carmichael numbers to exactly two bases.

221, 323, 899, 935, 1105, 1147, 1271, 1591, 1595, 1885, 2093, 2465, 2821, 4757, 4807, 4991, 5609, 5963, 6497, 7081, 7843, 9991, 10373, 10403, 10961, 11009, 12319, 13843, 14111, 16031, 17155, 17399, 17653, 17963, 19043, 19721, 20701, 24613, 27331, 28417, 29341

Offset: 1

Author

Tim Johannes Ohrtmann, May 07 2015

Keywords

• nonn

Examples

			a(1) = 221 because this is the first squarefree composite number n such that exactly two integers b except 0 exist such that for every prime factor p of n, p+b divides n+b (-11, -5): 221=13*17 and 2, 6 both divide 210 and 8, 12 both divide 216.
		

Links

• Tim Johannes Ohrtmann, Table of n, a(n) for n = 1..1487

Crossrefs

Cf. A257750 (every number of bases).

Cf. A257751, A257753, A257754, A257755, A257756, A257757, A258842 (1 and 3 to 8 bases).

Cf. A257758 (first occurrences).

Programs

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==2, print1(n, ", ")))))