A143957 An integer >= 2 is included if {the difference between the largest and smallest primes dividing n} divides n+1.

6, 12, 14, 15, 18, 20, 24, 35, 36, 39, 44, 45, 48, 50, 54, 63, 72, 75, 80, 84, 96, 108, 119, 135, 143, 144, 147, 152, 153, 155, 162, 175, 192, 200, 208, 216, 224, 225, 230, 231, 242, 245, 275, 279, 288, 294, 299, 315, 320, 323, 324, 374, 375, 384, 399, 405, 429

Offset: 1

Author

Leroy Quet, Sep 05 2008

Keywords

• nonn

Examples

			The largest prime dividing 14 is 7. The smallest prime dividing 14 is 2. 7-2=5 divides 14+1=15. So 14 is in the sequence.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A143958. Includes A037074.

Programs

Maple

filter:= proc(n) local P;
  P:= numtheory:-factorset(n);
  if nops(P) = 1 then return false fi;
  n+1 mod (max(P)-min(P)) = 0
end proc:
select(filter, [$2..1000]); # Robert Israel, Nov 04 2020

Mathematica

Select[Range[2, 429], If[Or[PrimeQ[#], PrimePowerQ[#]], False, Mod[#1, Last[#2] - First[#2]] == 0 & @@ {# + 1, FactorInteger[#][[All, 1]]}] &] (* Michael De Vlieger, Nov 04 2020 *)

Extensions

Extended by Ray Chandler, Nov 07 2008