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

Author

Tim Johannes Ohrtmann, May 07 2015

Keywords

• nonn

Comments

See A259238 for the corresponding bases.

Examples

			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.
		

Links

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

Crossrefs

Cf. A257750 (every number of bases).

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

Cf. A257758 (first occurrences).

Programs

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, ", ")))))