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A003593 Numbers of the form 3^i*5^j with i, j >= 0. 31
1, 3, 5, 9, 15, 25, 27, 45, 75, 81, 125, 135, 225, 243, 375, 405, 625, 675, 729, 1125, 1215, 1875, 2025, 2187, 3125, 3375, 3645, 5625, 6075, 6561, 9375, 10125, 10935, 15625, 16875, 18225, 19683, 28125, 30375, 32805, 46875, 50625, 54675, 59049 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Odd 5-smooth numbers (A051037). - Reinhard Zumkeller, Sep 18 2005

LINKS

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

FORMULA

a(n) ~ 1/sqrt(15)*exp(sqrt(2*log(3)*log(5)*n)) asymptotically. - Benoit Cloitre, Jan 22 2002

MAPLE

isA003593 := proc(n)

    if n = 1 then

        true;

    else

        return (numtheory[factorset](n) minus {3, 5} = {} );

    end if;

end proc:

A003593 := proc(n)

    option remember;

    if n = 1 then

        1;

    else

        for a from procname(n-1)+1 do

            if isA003593(a) then

                return a;

            end if;

        end do:

    end if;

end proc:

seq(A003593(n), n=1..30) ; # R. J. Mathar, Aug 04 2016

MATHEMATICA

fQ[n_] := PowerMod[15, n, n] == 0; Select[Range[60000], fQ] (* Bruno Berselli, Sep 24 2012 *)

PROG

(PARI) list(lim)=my(v=List(), N); for(n=0, log(lim)\log(5), N=5^n; while(N<=lim, listput(v, N); N*=3)); vecsort(Vec(v)) \\ Charles R Greathouse IV, Jun 28 2011

(PARI) is(n)=n==3^valuation(n, 3)*5^valuation(n, 5) \\ Charles R Greathouse IV, Apr 23 2013

(Haskell)

import Data.Set (singleton, deleteFindMin, insert)

a003593 n = a003593_list !! (n-1)

a003593_list = f (singleton 1) where

   f s = m : f (insert (3*m) $ insert (5*m) s') where

     (m, s') = deleteFindMin s

-- Reinhard Zumkeller, Sep 13 2011

(MAGMA) [n: n in [1..60000] | PrimeDivisors(n) subset [3, 5]]; // Bruno Berselli, Sep 24 2012

CROSSREFS

Cf. A033849, A112751-A112756, A143202.

Cf. A264997 (partitions into), see also A264998.

Sequence in context: A057235 A057289 A056754 * A120027 A018586 A135342

Adjacent sequences:  A003590 A003591 A003592 * A003594 A003595 A003596

KEYWORD

nonn

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified December 4 05:11 EST 2016. Contains 278748 sequences.