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

1, 12, 24, 36, 48, 60, 72, 96, 108, 120, 144, 168, 180, 192, 216, 240, 288, 300, 324, 336, 360, 384, 432, 480, 504, 540, 576, 600, 648, 660, 672, 720, 768, 840, 864, 900, 960, 972, 1008, 1080, 1152, 1176, 1200, 1296, 1320, 1344, 1440, 1500, 1512, 1536, 1620

Offset

1,2

Comments

Every term is a multiple of 12.

Links

Reinhard Zumkeller, Table of n, a(n) for n = 1..1000

Example

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.

Mathematica

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

Prog

(Haskell)
a141766 n = a141766_list !! (n-1)
a141766_list = filter f [1..] where
   f x = all (== 0) $ map (mod x) $ (map pred ps) ++ (map succ ps)
         where ps = a027748_row x
-- Reinhard Zumkeller, Aug 27 2013

Crossrefs

Cf. A140470, A141767, A124240.

Cf. A027748.

Sequence in context: A044837 A033009 A140470 * A367338 A069056 A359434

Adjacent sequences: A141763 A141764 A141765 * A141767 A141768 A141769

Keyword

nonn

Author

Leroy Quet, Jul 02 2008

Extensions

a(12)-a(50) from Donovan Johnson, Sep 27 2008

a(1)=1 prepended by Max Alekseyev, Aug 27 2013

Status

approved