A141766 - OEIS

%I #17 Sep 23 2017 03:20:42

%S 1,12,24,36,48,60,72,96,108,120,144,168,180,192,216,240,288,300,324,

%T 336,360,384,432,480,504,540,576,600,648,660,672,720,768,840,864,900,

%U 960,972,1008,1080,1152,1176,1200,1296,1320,1344,1440,1500,1512,1536,1620

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

%C Every term is a multiple of 12.

%H Reinhard Zumkeller, <a href="/A141766/b141766.txt">Table of n, a(n) for n = 1..1000</a>

%e 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 Select[Range[2, 1620], Function[n, AllTrue[FactorInteger[n][[All, 1]], AllTrue[# + {-1, 1}, Divisible[n, #] &] &]]] (* _Michael De Vlieger_, Sep 22 2017 *)

%o (Haskell)

%o a141766 n = a141766_list !! (n-1)

%o a141766_list = filter f [1..] where

%o    f x = all (== 0) $ map (mod x) $ (map pred ps) ++ (map succ ps)

%o          where ps = a027748_row x

%o -- _Reinhard Zumkeller_, Aug 27 2013

%Y Cf. A140470, A141767, A124240.

%Y Cf. A027748.

%K nonn

%O 1,2

%A _Leroy Quet_, Jul 02 2008

%E a(12)-a(50) from _Donovan Johnson_, Sep 27 2008

%E a(1)=1 prepended by _Max Alekseyev_, Aug 27 2013