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A259282 Quasi-Carmichael numbers to at least one negative base. 5
35, 77, 143, 187, 209, 221, 247, 299, 323, 391, 437, 493, 527, 561, 589, 713, 899, 943, 989, 1073, 1105, 1147, 1189, 1247, 1271, 1295, 1333, 1517, 1537, 1591, 1595, 1705, 1729, 1739, 1763, 1829, 1927, 1961, 2021, 2093, 2257, 2279, 2419, 2465, 2479, 2501, 2623 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Tim Johannes Ohrtmann, Table of n, a(n) for n = 1..100000

EXAMPLE

a(1) = 35 because this is the first squarefree composite number n such that at least one negative integer b exists such that for every prime factor p of n applies that p+b divides n+b (-3): 35=5*7 and 2, 4 both divide 32.

PROG

(PARI) for(n=2, 1000000, if(!isprime(n), if(issquarefree(n), f=factor(n); b=-f[1, 1]; until(c==0 || b==-1, b++; c=0; for(i=1, #f[, 1], if((n+b)%(f[i, 1]+b)>0, c++)); if(c==0, print1(n, ", "))))))

CROSSREFS

Cf. A257750, A257759, A259283.

Sequence in context: A300160 A257750 A257751 * A201068 A111144 A267555

Adjacent sequences:  A259279 A259280 A259281 * A259283 A259284 A259285

KEYWORD

nonn

AUTHOR

Tim Johannes Ohrtmann, Jun 23 2015

STATUS

approved

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Last modified June 20 12:24 EDT 2021. Contains 345164 sequences. (Running on oeis4.)