Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%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