A257751 Quasi-Carmichael numbers to exactly one base.

35, 77, 143, 165, 187, 209, 231, 247, 273, 299, 357, 391, 399, 437, 493, 527, 561, 589, 598, 713, 715, 943, 989, 1015, 1073, 1189, 1247, 1295, 1333, 1537, 1547, 1705, 1729, 1739, 1829, 1886, 1927, 1961, 2015, 2021, 2257, 2279, 2387, 2397, 2419, 2451, 2479, 2501

Offset

1,1

Comments

See A259238 for the corresponding bases.

Links

Tim Johannes Ohrtmann, Table of n, a(n) for n = 1..14688

Example

a(1) = 35 because this is the first squarefree composite number n such that exactly one nonzero integer b exists such that for every prime factor p of n, 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); 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==1, print1(n, ", ")))))

Crossrefs

Cf. A257750 (every number of bases).

Cf. A257752, A257753, A257754, A257755, A257756, A257757, A258842 (2 to 8 bases).

Cf. A257758 (first occurrences).

Sequence in context: A254443 A300160 A257750 * A259282 A201068 A111144

Adjacent sequences: A257748 A257749 A257750 * A257752 A257753 A257754

Keyword

nonn

Author

Tim Johannes Ohrtmann, May 07 2015

Status

approved