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A141767 A positive integer n is included if (p-1)*(p+1) divides n for every prime p that divides n. 4
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

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

Sequence lists the only numbers a(n) such that the average of a(n) consecutive Fibonacci numbers is always an integer. - Paolo P. Lava, Dec 22 2014

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

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Last modified October 20 11:46 EDT 2021. Contains 348100 sequences. (Running on oeis4.)