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A257759 Quasi-Carmichael numbers to at least one negative base and at least one positive base. 4
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified February 27 11:19 EST 2021. Contains 341653 sequences. (Running on oeis4.)