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

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.

Sequence in context: A310671 A310672 A310673 * A286303 A084336 A094750

Adjacent sequences: A171661 A171662 A171663 * A171665 A171666 A171667

Keyword

nonn

Author

Vladimir Joseph Stephan Orlovsky, Dec 14 2009

Status

approved