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A033846 Numbers whose prime factors are 2 and 5. 19
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

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

LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

FORMULA

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

MAPLE

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

MATHEMATICA

Take[Union[Times@@@Select[Flatten[Table[Tuples[{2, 5}, n], {n, 2, 15}], 1], Length[Union[#]]>1&]], 45] (* Harvey P. Dale, Dec 15 2011 *)

PROG

(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

CROSSREFS

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

KEYWORD

nonn,easy

AUTHOR

Jeff Burch

EXTENSIONS

Offset fixed by Reinhard Zumkeller, Sep 13 2011

STATUS

approved

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Last modified December 5 19:04 EST 2022. Contains 358588 sequences. (Running on oeis4.)