%I #12 Sep 08 2022 08:46:10

%S 1,4,8,16,21,27,35,36,55,57,63,64,65,75,77,85,98,100,111,119,125,128,

%T 133,143,144,155,161,171,183,189,203,205,209,215,235,237,242,243,245,

%U 253,259,275,291,301,305,323,324,333,335,338,343,351,355,365,377,391

%N Nonprime numbers n such that sigma(n) + n is prime.

%C Complement of A005384 (Sophie Germain primes) with respect to A078762 (numbers n such that n + sigma(n) is prime).

%e Number 8 is in sequence because sigma(8)+8 = 15+8 = 23 (prime).

%p select(n -> not isprime(n) and isprime(n + numtheory:-sigma(n)), [$1..1000]); # _Robert Israel_, Nov 13 2014

%t Select[Range[500], PrimeQ[DivisorSigma[1, #] + #]&& !PrimeQ[#] &] (* _Vincenzo Librandi_, Nov 14 2014 *)

%o (Magma) [n: n in[1..10000] | IsPrime(SumOfDivisors(n)+ n) and not IsPrime(n) ]

%o (PARI) print1(1,", ");forcomposite(n=1,1000,if(isprime(sigma(n)+n),print1(n,", "))) \\ _Derek Orr_, Nov 13 2014

%Y Cf. A000040, A000203, A018252, A005384, A078762.

%K nonn,easy

%O 1,2

%A _Jaroslav Krizek_, Nov 13 2014