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A141766 A positive integer n is included if both (p-1) and (p+1) divide n for every prime p that divides n.

%I A141766 #17 Sep 23 2017 03:20:42
%S A141766 1,12,24,36,48,60,72,96,108,120,144,168,180,192,216,240,288,300,324,
%T A141766 336,360,384,432,480,504,540,576,600,648,660,672,720,768,840,864,900,
%U A141766 960,972,1008,1080,1152,1176,1200,1296,1320,1344,1440,1500,1512,1536,1620
%N A141766 A positive integer n is included if both (p-1) and (p+1) divide n for every prime p that divides n.
%C A141766 Every term is a multiple of 12.
%H A141766 Reinhard Zumkeller, <a href="/A141766/b141766.txt">Table of n, a(n) for n = 1..1000</a>
%e A141766 120 has the prime factorization of 2^3 * 3^1 * 5^1. The distinct primes dividing 120 are therefore 2,3,5. 2-1=1, 3-1=2 and 5-1=4 all divide 120. Also, 2+1=3, 3+1=4 and 5+1=6 all divide 120. So 120 is included in the sequence.
%t A141766 Select[Range[2, 1620], Function[n, AllTrue[FactorInteger[n][[All, 1]], AllTrue[# + {-1, 1}, Divisible[n, #] &] &]]] (* _Michael De Vlieger_, Sep 22 2017 *)
%o A141766 (Haskell)
%o A141766 a141766 n = a141766_list !! (n-1)
%o A141766 a141766_list = filter f [1..] where
%o A141766    f x = all (== 0) $ map (mod x) $ (map pred ps) ++ (map succ ps)
%o A141766          where ps = a027748_row x
%o A141766 -- _Reinhard Zumkeller_, Aug 27 2013
%Y A141766 Cf. A140470, A141767, A124240.
%Y A141766 Cf. A027748.
%K A141766 nonn
%O A141766 1,2
%A A141766 _Leroy Quet_, Jul 02 2008
%E A141766 a(12)-a(50) from _Donovan Johnson_, Sep 27 2008
%E A141766 a(1)=1 prepended by _Max Alekseyev_, Aug 27 2013