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A257756 Quasi-Carmichael numbers to exactly six bases. 9
189029, 404471, 424663, 2595221, 4140901, 4197377, 4347209, 4528159, 4566193, 4631023, 4708819, 4864411, 5175589, 5311729, 6380651, 6400819, 6426029, 7117783, 8173877, 8915971, 10080589, 10460869, 10671173, 11094661, 11538313 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
LINKS
EXAMPLE
a(1) = 189029 because this is the first squarefree composite number n such that exactly six integers b except 0 exist such that for every prime factor p of n, p+b divides n+b (-419, -414, -407, -389, -365, -309): 189029=421*449 and 2, 30 both divide 188610 and 7, 35 both divide 188615 and 14, 42 both divide 188622 and 32, 60 both divide 188640 and 56, 84 both divide 188664 and 112, 140 both divide 188720.
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==6, print1(n, ", ")))))
CROSSREFS
Cf. A257750 (every number of bases).
Cf. A257751, A257752, A257753, A257754, A257755, A257757, A258842 (1, 2, 3, 4, 5, 7 and 8 bases).
Cf. A257758 (first occurrences).
Sequence in context: A233715 A110069 A006028 * A206018 A233873 A256768
KEYWORD
nonn
AUTHOR
STATUS
approved

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Last modified February 21 14:36 EST 2024. Contains 370235 sequences. (Running on oeis4.)