A141767 A positive integer k is included if (p-1)*(p+1) divides k for every prime p that divides k.
1, 24, 48, 72, 96, 120, 144, 192, 216, 240, 288, 336, 360, 384, 432, 480, 576, 600, 648, 672, 720, 768, 864, 960, 1008, 1080, 1152, 1200, 1296, 1320, 1344, 1440, 1536, 1680, 1728, 1800, 1920, 1944, 2016, 2160, 2304, 2352, 2400, 2592, 2640, 2688, 2880, 3000
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)*(2+1)=3, (3-1)*(3+1)=8 and (5-1)*(5+1)=24 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
a141767 n = a141767_list !! (n-1) a141767_list = filter f [1..] where f x = all (== 0) $ map (mod x) $ zipWith (*) (map pred ps) (map succ ps) where ps = a027748_row x -- Reinhard Zumkeller, Aug 27 2013 -
Mathematica
fQ[n_] := Block[{p = First /@ FactorInteger@ n}, Union@ Mod[n, (p - 1) (p + 1)] == {0}]; Select[ Range[2, 3000], fQ@# &] (* Robert G. Wilson v, May 25 2009 *)
Extensions
Added missing term 336 and a(14)-a(47) from Donovan Johnson, Sep 27 2008
a(1)=1 prepended by Max Alekseyev, Aug 27 2013
Comments