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A033846
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Numbers whose prime factors are 2 and 5.
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19
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10, 20, 40, 50, 80, 100, 160, 200, 250, 320, 400, 500, 640, 800, 1000, 1250, 1280, 1600, 2000, 2500, 2560, 3200, 4000, 5000, 5120, 6250, 6400, 8000, 10000, 10240, 12500, 12800, 16000, 20000, 20480, 25000, 25600, 31250, 32000, 40000, 40960
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OFFSET
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1,1
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COMMENTS
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Numbers k such that Sum_{d prime divisor of k} 1/d = 7/10. - Benoit Cloitre, Apr 13 2002
Numbers k such that phi(k) = (2/5)*k. - Benoit Cloitre, Apr 19 2002
Numbers k such that Sum_{d|k} A008683(d)*A000700(d) = 7. - Carl Najafi, Oct 20 2011
k-th cyclotomic polynomial with exactly 2 negative coefficients (see A086780). - Paolo P. Lava, May 10 2019
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LINKS
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Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
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FORMULA
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a(n) = 10*A003592(n).
A143201(a(n)) = 4. - Reinhard Zumkeller, Sep 13 2011
Sum_{n>=1} 1/a(n) = 1/4. - Amiram Eldar, Dec 22 2020
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MAPLE
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A033846 := proc(n)
if (numtheory[factorset](n) = {2, 5}) then
RETURN(n)
fi: end: seq(A033846(n), n=1..50000); # Jani Melik, Feb 24 2011
# Alternate
with(numtheory): P:=proc(n) local x; if nops(select(x->x<0, [coeffs(cyclotomic(n, x))]))=2 then n; fi; end: seq(P(j), j=1..40960); # Paolo P. Lava, May 10 2019
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MATHEMATICA
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Take[Union[Times@@@Select[Flatten[Table[Tuples[{2, 5}, n], {n, 2, 15}], 1], Length[Union[#]]>1&]], 45] (* Harvey P. Dale, Dec 15 2011 *)
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PROG
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(PARI) isA033846(n)=factor(n)[, 1]==[2, 5]~ \\ Charles R Greathouse IV, Feb 24 2011
(Haskell)
import Data.Set (singleton, deleteFindMin, insert)
a033846 n = a033846_list !! (n-1)
a033846_list = f (singleton (2*5)) where
f s = m : f (insert (2*m) $ insert (5*m) s') where
(m, s') = deleteFindMin s
-- Reinhard Zumkeller, Sep 13 2011
(Magma) [n:n in [1..100000]| Set(PrimeDivisors(n)) eq {2, 5}]; // Marius A. Burtea, May 10 2019
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CROSSREFS
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Cf. A033845, A033847, A033848, A033849, A033850, A033851, A003592.
Cf. A086780, A143201.
Cf. A000700, A008683.
Sequence in context: A172172 A275245 A020953 * A114931 A013978 A241608
Adjacent sequences: A033843 A033844 A033845 * A033847 A033848 A033849
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KEYWORD
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nonn,easy
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AUTHOR
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Jeff Burch
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EXTENSIONS
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Offset fixed by Reinhard Zumkeller, Sep 13 2011
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STATUS
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approved
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