A257759 Quasi-Carmichael numbers to at least one negative base and at least one positive base.

1105, 1595, 2093, 2465, 2821, 7843, 10373, 17963, 19721, 29341, 31003, 33143, 46189, 46657, 62647, 66263, 70151, 70219, 88559, 101813, 106361, 115843, 193343, 200777, 206471, 209933, 230159, 234883, 252601, 285619, 294409, 308267, 343027, 369799, 423181, 467273

Offset

1,1

Comments

It is a open question whether any Carmichael number exists that is also a Lucas-Carmichael number.

Links

Tim Johannes Ohrtmann, Table of n, a(n) for n = 1..130

Example

a(1) = 1105 because this is the first squarefree composite number n such that at least one negative integer and at least one positive integer except 0 exist such that for every prime factor p of n applies that p+b divides n+b (-1, 15): 1105=5*13*17 and 4, 12, 16 both divide 1104 and 20, 28, 32 both divide 1120.

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, if(k==0, k++), if(b>0, if(k==1, k++))))); if(k==2, print1(n, ", ")))))

Crossrefs

Intersection of A259282 and A259283.

Sequence in context: A175521 A214607 A321870 * A025295 A025314 A025287

Adjacent sequences: A257756 A257757 A257758 * A257760 A257761 A257762

Keyword

nonn

Author

Tim Johannes Ohrtmann, May 12 2015

Status

approved