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

Author

Tim Johannes Ohrtmann, May 12 2015

Keywords

• nonn

Examples

			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.
		

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).

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