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

Author

Tim Johannes Ohrtmann, May 12 2015

Keywords

• nonn

Examples

			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.
		

Links

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

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).

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