A257755 Quasi-Carmichael numbers to exactly five bases.

34933, 295927, 312157, 346777, 379231, 417091, 444853, 471773, 576077, 582133, 1384753, 1462579, 1687397, 1689991, 1713337, 1861289, 1944869, 3211183, 3654223, 4092493, 4358737, 5134531, 5410051, 5564557, 6863671, 7061321, 7343659, 7531889, 7622221, 7817591

Offset

1,1

Links

Table of n, a(n) for n=1..30.

Example

a(1) = 34933 because this is the first squarefree composite number n such that exactly five integers except 0 exist such that for every prime factor p of n applies that p+b divides n+b (-178, -175, -173, -157, -133): 34933=181*193 and 3, 15 both divide 34755 and 6, 18 both divide 34758 and 18, 20 both divide 34760 and 24, 36 both divide 34776 and 48, 60 both divide 34800.

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==5, print1(n, ", ")))))

Crossrefs

Cf. A257750 (every number of bases).

Cf. A257751, A257752, A257753, A257754, A257756, A257757, A258842 (1, 2, 3, 4, 6, 7 and 8 bases).

Cf. A257758 (first occurrences).

Sequence in context: A233815 A247695 A204886 * A230976 A085847 A319589

Adjacent sequences: A257752 A257753 A257754 * A257756 A257757 A257758

Keyword

nonn

Author

Tim Johannes Ohrtmann, May 12 2015

Status

approved