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%I #43 Mar 18 2017 08:48:53
%S 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,
%T 74,78,80,84,86,88,90,94,96,98,100,104,110,112,114,118,122,126,128,
%U 130,132,134,136,140,142,146,148,152,156,158,162,164,168,172,174,182,190,194,196,200,202
%N 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.
%C Terms are all even for n > 3.
%C 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.
%H Charles R Greathouse IV, <a href="/A283022/b283022.txt">Table of n, a(n) for n = 1..10000</a>
%e 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.
%t 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 *)
%o (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
%Y 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).
%K nonn
%O 1,2
%A _Juri-Stepan Gerasimov_, Mar 15 2017
%E Corrected by _Charles R Greathouse IV_, Mar 15 2017
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