A257754 Quasi-Carmichael numbers to exactly four bases.

60491, 61937, 65311, 76151, 116843, 127723, 159197, 164009, 168821, 194417, 272483, 284987, 329467, 364087, 369857, 370817, 385241, 389327, 395497, 407837, 423701, 431393, 465043, 509461, 613927, 837209, 853607, 881717, 999919, 1041541, 1117213, 1279903, 1294819

Offset

1,1

Links

Tim Johannes Ohrtmann, Table of n, a(n) for n = 1..145

Example

a(1) = 60491 because this is the first squarefree composite number n such that exactly four integers b except 0 exist such that for every prime factor p of n, p+b divides n+b (-239, -236, -231, -191): 60491=241*251 and 2, 12 both divide 60252 and 5, 15 both divide 60255 and 10, 20 both divide 60260 and 50, 60 both divide 60300.

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==4, print1(n, ", ")))))

Crossrefs

Cf. A257750 (every number of bases).

Cf. A257751, A257752, A257753, A257755, A257756, A257757, A258842 (1, 2, 3, 5, 6, 7 and 8 bases).

Cf. A257758 (first occurrences).

Sequence in context: A186556 A205983 A218488 * A234767 A186061 A237305

Adjacent sequences: A257751 A257752 A257753 * A257755 A257756 A257757

Keyword

nonn

Author

Tim Johannes Ohrtmann, May 12 2015

Status

approved