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

1,1

Links

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

Example

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.

Prog

(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, ", ")))))

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).

Sequence in context: A345512 A048931 A052478 * A147284 A171427 A211817

Adjacent sequences: A257749 A257750 A257751 * A257753 A257754 A257755

Keyword

nonn

Author

Tim Johannes Ohrtmann, May 07 2015

Status

approved