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A258842
Quasi-Carmichael numbers to exactly eight bases.
10
182293, 6536953, 13116283, 23337661, 55898473, 56624329, 66112261, 66355291, 66846751, 67239919, 75289033, 76222261, 93331321, 97594157, 110397013, 115175383, 146385797, 147111617, 157333573, 158029141, 159289241, 163825601, 181950817, 187826449, 207820831
OFFSET
1,1
COMMENTS
All known terms have only two prime factors whereby the second prime factor is only slightly larger than the first.
a(3384) > 10^12. - Hiroaki Yamanouchi, Sep 26 2015
LINKS
EXAMPLE
a(1) = 182293 because this is the first squarefree composite number n such that exactly eight integers except 0 exist such that for every prime factor p of n applies that p+b divides n+b (-419, -418, -413, -412, -405, -403, -373, -349): 182293=421*433 and 2, 14 both divide 181874 and 3, 15 both divide 181875 and 8, 20 both divide 181880 and 9, 21 both divide 181881 and 16, 28 both divide 181888 and 18, 30 both divide 181890 and 48, 60 both divide 181920 and 72, 84 both divide 181944.
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==8, print1(n, ", ")))))
CROSSREFS
Cf. A257750 (every number of bases).
Cf. A257758 (first occurrences).
Sequence in context: A375118 A249959 A250013 * A368939 A030466 A233956
KEYWORD
nonn
AUTHOR
EXTENSIONS
a(4)-a(25) from Hiroaki Yamanouchi, Sep 26 2015
STATUS
approved