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

1,1

Links

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

Example

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.

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==3, print1(n, ", ")))))

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).

Sequence in context: A252508 A031810 A020415 * A236724 A206654 A356767

Adjacent sequences: A257750 A257751 A257752 * A257754 A257755 A257756

Keyword

nonn

Author

Tim Johannes Ohrtmann, May 07 2015

Status

approved