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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 (list; graph; refs; listen; history; text; internal format)
 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 Hiroaki Yamanouchi, Table of n, a(n) for n = 1..3383 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. A257751, A257752, A257753, A257754, A257755, A257756, A257757 (1 to 7 bases). Cf. A257758 (first occurrences). Sequence in context: A145536 A249959 A250013 * A030466 A233956 A249232 Adjacent sequences:  A258839 A258840 A258841 * A258843 A258844 A258845 KEYWORD nonn AUTHOR Tim Johannes Ohrtmann, Jun 12 2015 EXTENSIONS a(4)-a(25) from Hiroaki Yamanouchi, Sep 26 2015 STATUS approved

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Last modified January 17 22:33 EST 2022. Contains 350410 sequences. (Running on oeis4.)