A259282 Quasi-Carmichael numbers to at least one negative base.

35, 77, 143, 187, 209, 221, 247, 299, 323, 391, 437, 493, 527, 561, 589, 713, 899, 943, 989, 1073, 1105, 1147, 1189, 1247, 1271, 1295, 1333, 1517, 1537, 1591, 1595, 1705, 1729, 1739, 1763, 1829, 1927, 1961, 2021, 2093, 2257, 2279, 2419, 2465, 2479, 2501, 2623

Offset

1,1

Links

Tim Johannes Ohrtmann, Table of n, a(n) for n = 1..100000

Example

a(1) = 35 because this is the first squarefree composite number n such that at least one negative integer b exists such that for every prime factor p of n applies that p+b divides n+b (-3): 35=5*7 and 2, 4 both divide 32.

Prog

(PARI) for(n=2, 1000000, if(!isprime(n), if(issquarefree(n), f=factor(n); b=-f[1, 1]; until(c==0 || b==-1, 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, A259283.

Sequence in context: A300160 A257750 A257751 * A201068 A111144 A267555

Adjacent sequences: A259279 A259280 A259281 * A259283 A259284 A259285

Keyword

nonn

Author

Tim Johannes Ohrtmann, Jun 23 2015

Status

approved