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A283022
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Numbers n such that the number of primes of the form n - x is not equal to the number of primes of the form n + y where x, y are divisors of n.
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1
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1, 2, 3, 4, 6, 8, 14, 16, 20, 24, 26, 28, 32, 34, 36, 38, 40, 44, 48, 52, 54, 62, 66, 68, 70, 74, 78, 80, 84, 86, 88, 90, 94, 96, 98, 100, 104, 110, 112, 114, 118, 122, 126, 128, 130, 132, 134, 136, 140, 142, 146, 148, 152, 156, 158, 162, 164, 168, 172, 174, 182, 190, 194, 196, 200, 202
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OFFSET
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1,2
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COMMENTS
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Terms are all even for n > 3.
Sophie Germain primes > 3 such that the number of primes of the form 2p - x is equal to the number of primes of the form 2p + y where x, y are divisors of 2p.
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LINKS
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EXAMPLE
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3 is in this sequence because 3 - 1 = 2 is prime and 3 - 3 = 0, but 3 + 1 = 4 and 3 + 3 = 6, where 1, 3 are divisors of 3 and 0, 4, 6 are nonprimes.
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MATHEMATICA
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p[n_]:=If[PrimeQ[n], 1, 0]; Select[Range@ 202, Sum[p[# - d], {d, Divisors[Factor[#]]}] != Sum[p[# + d], {d, Divisors[Factor[#]]}] &] (* Indranil Ghosh, Mar 15 2017 *)
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PROG
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(PARI) is(n)=my(f=factor(n)); sumdiv(f, d, isprime(n-d)) != sumdiv(f, d, isprime(n+d)) \\ Charles R Greathouse IV, Mar 15 2017
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CROSSREFS
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Cf. A005384 (Sophie Germain primes), A005382 (primes p such that number of primes of the form 2p - m is equal to exactly two, where m is divisor of p).
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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