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 A257753 Quasi-Carmichael numbers to exactly three bases. 10
 1517, 1763, 4331, 4453, 5183, 5767, 9797, 10573, 12317, 14351, 16637, 34571, 35657, 38021, 38191, 38407, 40723, 41989, 50429, 50851, 57599, 67721, 70151, 75067, 79523, 87953, 111547, 117613, 150463, 159559, 167137, 173633, 181451, 190087, 191819, 197881, 205193 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 LINKS Tim Johannes Ohrtmann, Table of n, a(n) for n = 1..403 EXAMPLE a(1) = 1517 because this is the first squarefree composite number n such that exactly three integers b except 0 exist such that for every prime factor p of n, p+b divides n+b (-35, -32, -29): 1517=37*41 and 2, 6 both divide 1482 and 5, 9 both divide 1485 and 8, 12 divide 1488. 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==3, print1(n, ", "))))) CROSSREFS Cf. A257750 (every number of bases). Cf. A257751, A257752, A257754, A257755, A257756, A257757, A258842 (1, 2, 4, 5, 6, 7 and 8 bases). Cf. A257758 (first occurrences). Sequence in context: A252508 A031810 A020415 * A236724 A206654 A112641 Adjacent sequences:  A257750 A257751 A257752 * A257754 A257755 A257756 KEYWORD nonn AUTHOR Tim Johannes Ohrtmann, May 07 2015 STATUS approved

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Last modified November 27 01:16 EST 2021. Contains 349344 sequences. (Running on oeis4.)