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A141767 A positive integer k is included if (p-1)*(p+1) divides k for every prime p that divides k.

%I A141767 #23 Mar 08 2024 01:12:10
%S A141767 1,24,48,72,96,120,144,192,216,240,288,336,360,384,432,480,576,600,
%T A141767 648,672,720,768,864,960,1008,1080,1152,1200,1296,1320,1344,1440,1536,
%U A141767 1680,1728,1800,1920,1944,2016,2160,2304,2352,2400,2592,2640,2688,2880,3000
%N A141767 A positive integer k is included if (p-1)*(p+1) divides k for every prime p that divides k.
%C A141767 For n>1, a(n) is a multiple of 24.
%H A141767 Reinhard Zumkeller, <a href="/A141767/b141767.txt">Table of n, a(n) for n = 1..1000</a>
%e A141767 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 A141767 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 A141767 (Haskell)
%o A141767 a141767 n = a141767_list !! (n-1)
%o A141767 a141767_list = filter f [1..] where
%o A141767    f x = all (== 0) $
%o A141767          map (mod x) $ zipWith (*) (map pred ps) (map succ ps)
%o A141767          where ps = a027748_row x
%o A141767 -- _Reinhard Zumkeller_, Aug 27 2013
%Y A141767 Cf. A140470, A141766, A124240.
%Y A141767 Cf. A027748, A084920.
%K A141767 nonn
%O A141767 1,2
%A A141767 _Leroy Quet_, Jul 02 2008
%E A141767 Added missing term 336 and a(14)-a(47) from _Donovan Johnson_, Sep 27 2008
%E A141767 a(1)=1 prepended by _Max Alekseyev_, Aug 27 2013