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A350705
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Composite numbers that have no Sophie Germain prime and no "safe prime" factors.
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3
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169, 221, 247, 289, 323, 361, 403, 481, 527, 559, 589, 629, 703, 731, 793, 817, 871, 923, 949, 961, 1027, 1037, 1139, 1147, 1159, 1207, 1241, 1261, 1273, 1313, 1333, 1339, 1343, 1349, 1369, 1387, 1417, 1501, 1591, 1649, 1651, 1717, 1751, 1781, 1807, 1843, 1849, 1853
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OFFSET
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1,1
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COMMENTS
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Prime factors of the terms have to be in A059500.
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LINKS
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EXAMPLE
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MATHEMATICA
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Select[Range[2000], CompositeQ[#] && AllTrue[FactorInteger[#][[;; , 1]], ! PrimeQ[2*#1 + 1] && ! PrimeQ[(#1 - 1)/2] &] &] (* Amiram Eldar, Feb 15 2022 *)
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PROG
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(Python)
from sympy import primefactors, isprime
print([n for n in range(2, 1854) if not isprime(n) and all(not isprime(p*2+1) and not isprime((p-1)//2) for p in primefactors(n))])
(PARI) isok(m) = if ((m>1) && !isprime(m), my(f=factor(m)[, 1]); !#select(x->isprime(2*x+1), f) && !#select(x->isprime((x-1)/2), f)); \\ Michel Marcus, Feb 14 2022
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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