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

1,2

Comments

For n>1, a(n) is a multiple of 24.

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)*(2+1)=3, (3-1)*(3+1)=8 and (5-1)*(5+1)=24 all divide 120. So 120 is included in the sequence.

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 *)

Prog

(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

Crossrefs

Cf. A140470, A141766, A124240.

Cf. A027748, A084920.

Sequence in context: A162282 A008606 A317971 * A327947 A288639 A280097

Adjacent sequences: A141764 A141765 A141766 * A141768 A141769 A141770

Keyword

nonn

Author

Leroy Quet, Jul 02 2008

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

Status

approved