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
Keywords
Examples
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.
Links
- Reinhard Zumkeller, Table of n, a(n) for n = 1..1000
Programs
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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 -
Mathematica
Select[Range[2, 1620], Function[n, AllTrue[FactorInteger[n][[All, 1]], AllTrue[# + {-1, 1}, Divisible[n, #] &] &]]] (* Michael De Vlieger, Sep 22 2017 *)
Extensions
a(12)-a(50) from Donovan Johnson, Sep 27 2008
a(1)=1 prepended by Max Alekseyev, Aug 27 2013
Comments