%I #10 Aug 30 2021 12:15:28

%S 4,6,9,14,18,21,27,57,69,77,141,155,161,194,261,381,428,551,579,620,

%T 626,671,672,704,720,755,1007,1349,1506,1529,1611,1659,1707,1710,1814,

%U 1982,1986,1994,2036,2037,2157,2429,2651,2714,2771,2783,2966,3039,3044,3101

%N Numbers k such that (Product_{d|k} d) - k - 1 and (Product_{d|k} d) + k + 1 are primes.

%e Divisors of 6: 1,2,3,6. As 6*3*2*1 = 36, 36 - 6 - 1 = 29 is prime, and 36 + 6 + 1 = 43 is prime, 6 is a term.

%t f[n_]:=PrimeQ[Times@@Divisors[n]-n-1]&&PrimeQ[Times@@Divisors[n]+n+1]; lst={};Do[If[f[n],AppendTo[lst,n]],{n,7!}];lst

%t Select[Range[3200],AllTrue[Times@@Divisors[#]+{(#+1),(-#-1)},PrimeQ]&] (* _Harvey P. Dale_, Aug 30 2021 *)

%Y Cf. A118369.

%K nonn

%O 1,1

%A _Vladimir Joseph Stephan Orlovsky_, Dec 14 2009