A171664 - OEIS

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A171664

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

4, 6, 9, 14, 18, 21, 27, 57, 69, 77, 141, 155, 161, 194, 261, 381, 428, 551, 579, 620, 626, 671, 672, 704, 720, 755, 1007, 1349, 1506, 1529, 1611, 1659, 1707, 1710, 1814, 1982, 1986, 1994, 2036, 2037, 2157, 2429, 2651, 2714, 2771, 2783, 2966, 3039, 3044, 3101

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OFFSET

1,1

LINKS

Table of n, a(n) for n=1..50.

EXAMPLE

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.

MATHEMATICA

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

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

CROSSREFS

Cf. A118369.