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A143207 Numbers with distinct prime factors 2, 3, and 5. 28
30, 60, 90, 120, 150, 180, 240, 270, 300, 360, 450, 480, 540, 600, 720, 750, 810, 900, 960, 1080, 1200, 1350, 1440, 1500, 1620, 1800, 1920, 2160, 2250, 2400, 2430, 2700, 2880, 3000, 3240, 3600, 3750, 3840, 4050, 4320, 4500, 4800, 4860 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
Numbers of the form 2^i * 3^j * 5^k with i, j, k > 0. - Reinhard Zumkeller, Sep 13 2011
Integers k such that phi(k)/k = 4/15. - Artur Jasinski, Nov 07 2008
LINKS
Vaclav Kotesovec, Table of n, a(n) for n = 1..10000 (terms 1..1000 from T. D. Noe)
FORMULA
A001221(a(n)) = 3; A020639(a(n)) = 2; A006530(a(n)) = 5; A143201(a(n)) = 6.
a(n) = 30*A051037(n); A007947(a(n)) = A010869(n). - Reinhard Zumkeller, Sep 13 2011
a(n) ~ sqrt(30) * exp((6*log(2)*log(3)*log(5)*n)^(1/3)). - Vaclav Kotesovec, Sep 22 2020
Sum_{n>=1} 1/a(n) = 1/8. - Amiram Eldar, Sep 24 2020
MATHEMATICA
a = {}; Do[If[EulerPhi[x]/x == 4/15, AppendTo[a, x]], {x, 1, 11664}]; a (* Artur Jasinski, Nov 07 2008 *)
n = 10^4; Table[2^i*3^j*5^k, {i, 1, Log[2, n]}, {j, 1, Log[3, n/2^i]}, {k, 1, Log[5, n/(2^i*3^j)]}] // Flatten // Sort (* Amiram Eldar, Sep 24 2020 *)
PROG
(Haskell)
import Data.Set (singleton, deleteFindMin, insert)
a143207 n = a143207_list !! (n-1)
a143207_list = f (singleton (2*3*5)) where
f s = m : f (insert (2*m) $ insert (3*m) $ insert (5*m) s') where
(m, s') = deleteFindMin s
-- Reinhard Zumkeller, Sep 13 2011
(PARI) list(lim)=my(v=List(), s, t); for(i=1, logint(lim\6, 5), t=5^i; for(j=1, logint(lim\t\2, 3), s=t*3^j; while((s<<=1)<=lim, listput(v, s)))); Set(v) \\ Charles R Greathouse IV, Sep 14 2015
(PARI) is(n) = if(n%30, return(0)); my(f=factor(n, 6)[, 1]); f[#f]<6 \\ David A. Corneth, Sep 22 2020
(Magma) [n: n in [1..5000] | PrimeDivisors(n) eq [2, 3, 5]]; // Bruno Berselli, Sep 14 2015
CROSSREFS
Cf. A069819.
Subsequence of A143204 and of A051037.
Sequence in context: A050519 A358756 A069819 * A359410 A108454 A235483
KEYWORD
nonn,easy
AUTHOR
Reinhard Zumkeller, Aug 12 2008
EXTENSIONS
New name from Charles R Greathouse IV, Sep 14 2015
STATUS
approved

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Last modified March 19 04:58 EDT 2024. Contains 370952 sequences. (Running on oeis4.)