%I #23 Mar 08 2024 01:12:10

%S 1,24,48,72,96,120,144,192,216,240,288,336,360,384,432,480,576,600,

%T 648,672,720,768,864,960,1008,1080,1152,1200,1296,1320,1344,1440,1536,

%U 1680,1728,1800,1920,1944,2016,2160,2304,2352,2400,2592,2640,2688,2880,3000

%N A positive integer k is included if (p-1)*(p+1) divides k for every prime p that divides k.

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

%H Reinhard Zumkeller, <a href="/A141767/b141767.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)*(2+1)=3, (3-1)*(3+1)=8 and (5-1)*(5+1)=24 all divide 120. So 120 is included in the sequence.

%t 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 *)

%o (Haskell)

%o a141767 n = a141767_list !! (n-1)

%o a141767_list = filter f [1..] where

%o f x = all (== 0) $

%o map (mod x) $ zipWith (*) (map pred ps) (map succ ps)

%o where ps = a027748_row x

%o -- _Reinhard Zumkeller_, Aug 27 2013

%Y Cf. A140470, A141766, A124240.

%Y Cf. A027748, A084920.

%K nonn

%O 1,2

%A _Leroy Quet_, Jul 02 2008

%E Added missing term 336 and a(14)-a(47) from _Donovan Johnson_, Sep 27 2008

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