A257753 Quasi-Carmichael numbers to exactly three bases.

1517, 1763, 4331, 4453, 5183, 5767, 9797, 10573, 12317, 14351, 16637, 34571, 35657, 38021, 38191, 38407, 40723, 41989, 50429, 50851, 57599, 67721, 70151, 75067, 79523, 87953, 111547, 117613, 150463, 159559, 167137, 173633, 181451, 190087, 191819, 197881, 205193

Offset: 1

Author

Tim Johannes Ohrtmann, May 07 2015

Keywords

• nonn

Examples

			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.
		

Links

• Tim Johannes Ohrtmann, Table of n, a(n) for n = 1..403

Crossrefs

Cf. A257750 (every number of bases).

Cf. A257751, A257752, A257754, A257755, A257756, A257757, A258842 (1, 2, 4, 5, 6, 7 and 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==3, print1(n, ", ")))))