A257758 Least Quasi-Carmichael number to exactly n bases.

35, 221, 1517, 60491, 34933, 189029, 777923, 182293, 11618977, 58076041, 268926877, 1047880741, 342323563, 447110449, 2987821321, 11951066641, 19719180049, 10178985781, 249381206761, 30512751277, 190703385391, 128931982141

Offset: 1

Author

Tim Johannes Ohrtmann, May 12 2015

Keywords

• nonn
• more

Comments

Is this sequence infinite?

10^12 < a(23) <= 4361890724227, a(24) = 805822195351 and a(25) = 560433369241.

Examples

			a(4) = 60491 because this is the first squarefree composite number n such that exactly four integers except 0 exist such that for every prime factor p of n applies that 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.
		

Links

• Hiroaki Yamanouchi, upper bounds of a(1)-a(65) (a(n) <= 10^20)

Crossrefs

Cf. A257750 (every number of bases).

Cf. A257751, A257752, A257753, A257754, A257755, A257756, A257757, A258842 (1 to 8 bases).

Programs

PARI

for(d=1,9, n=1; until(k==d, n++; 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==d, print1(n,", "))))))

Extensions

a(10)-a(22) from Hiroaki Yamanouchi, Sep 26 2015