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%I #17 Feb 24 2022 02:04:01
%S 1,2,6,10,14,24,26,54,56,74,88,94,134,146,154,174,206,238,248,266,296,
%T 314,326,328,374,378,386,430,442,466,472,488,494,498,510,568,582,584,
%U 634,674,680,710,730,742,786,856,874,894,918,962,986,1038,1094,1174
%N Numbers k such that 1 + Product_{d|k} d is prime.
%C See A118370 for the corresponding primes, 'divisorial primes'.
%H Paolo P. Lava, <a href="/A118369/b118369.txt">Table of n, a(n) for n = 1..10000</a>
%e The (positive) divisors of 6 are 1,2,3,6. As 6*3*2*1 + 1 = 37 is prime, 6 is a term.
%t f[n_]:=PrimeQ[Times@@Divisors[n]+1]; lst={};Do[If[f[n],AppendTo[lst,n]],{n,7!}];lst (* _Vladimir Joseph Stephan Orlovsky_, Dec 14 2009 *)
%o (PARI) for(n=1,2500, s=1; fordiv(n,d,s=s*d); if(isprime(s+1), print1(n,", ")))
%Y Cf. A118370, A007955.
%K nonn
%O 1,2
%A _Rick L. Shepherd_, Apr 25 2006