

A141767


A positive integer n is included if (p1)*(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
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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. (21)*(2+1)=3, (31)*(3+1)=8 and (51)*(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 !! (n1)
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



