A259283 Quasi-Carmichael numbers to at least one positive base.

165, 231, 273, 357, 399, 598, 715, 935, 1015, 1105, 1547, 1595, 1885, 1886, 2015, 2093, 2387, 2397, 2451, 2465, 2585, 2679, 2737, 2821, 2915, 3059, 3445, 3913, 3965, 4123, 4991, 5015, 5467, 5719, 6097, 6545, 7055, 7189, 7285, 7553, 7843, 8555, 8569, 8715, 8855

Offset

1,1

Links

Tim Johannes Ohrtmann, Table of n, a(n) for n = 1..2963

Example

a(1) = 165 because this is the first squarefree composite number n such that at least one positive integer b except 0 exists such that for every prime factor p of n applies that p+b divides n+b (3): 165=3*5*11 and 6, 8, 14 all divide 168.

Prog

(PARI) for(n=2, 1000000, if(!isprime(n), if(issquarefree(n), f=factor(n); b=0; until(c==0 || b==n, b++; c=0; for(i=1, #f[, 1], if((n+b)%(f[i, 1]+b)>0, c++)); if(c==0, print1(n, ", "))))))

Crossrefs

Cf. A257750, A257759, A259282.

Sequence in context: A252725 A168355 A083255 * A319502 A270175 A319328

Adjacent sequences: A259280 A259281 A259282 * A259284 A259285 A259286

Keyword

nonn

Author

Tim Johannes Ohrtmann, Jun 23 2015

Status

approved