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%I #23 Jan 02 2023 12:30:48
%S 1,2,3,4,5,10,11,12,15,18,22,23,24,27,29,30,32,34,39,41,42,45,52,53,
%T 54,56,57,58,63,64,68,69,76,83,84,87,89,93,96,108,110,113,115,131,142,
%U 144,147,150,152,153,156,162,165,168,170,172,173,175,177
%N Numbers n such that d(n)*n + 1 is prime, d(n) = number of divisors of n.
%C This is the union of Sophie Germain primes and Sophie Germain nonprimes, so it might be called "Sophie Germain numbers".
%H Harvey P. Dale, <a href="/A210495/b210495.txt">Table of n, a(n) for n = 1..1000</a>
%H J. S. Gerasimov, <a href="http://list.seqfan.eu/oldermail/seqfan/2013-January/010687.html">Sophie Germain nonprimes</a> [title corrected], SeqFan mailing list, Jan 15 2013.
%p A210495 := proc(n)
%p option remember;
%p local a;
%p if n = 1 then
%p 1 ;
%p else
%p for a from procname(n-1)+1 do
%p if isprime(numtheory[tau](a)*a+1) then
%p return a;
%p end if;
%p end do:
%p end if;
%p end proc: # _R. J. Mathar_, Jan 27 2013
%t Select[Range[200],PrimeQ[# DivisorSigma[0,#]+1]&] (* _Harvey P. Dale_, Aug 26 2013 *)
%o (PARI) is(n)=isprime(numdiv(n)*n+1) \\ _Charles R Greathouse IV_, Jan 24 2013
%Y Cf. A083271, A005384, A209271, A000005.
%K nonn
%O 1,2
%A _Juri-Stepan Gerasimov_, Jan 24 2013
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