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 A003593 Numbers of the form 3^i*5^j with i, j >= 0. 32
 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 The characteristic function of this sequence is given by Sum_{n >= 1} x^a(n) = Sum_{n >= 1} mu(15*n)*x^n/(1 - x^n), where mu(n) is the Möbius function A008683. Cf. with the formula of Hanna in A051037. - Peter Bala, Mar 18 2019 Sum_{n>=1} 1/a(n) = (3*5)/((3-1)*(5-1)) = 15/8. - Amiram Eldar, Sep 22 2020 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 (GAP) Filtered([1..60000], n->PowerMod(15, n, n)=0); # Muniru A Asiru, Mar 19 2019 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,changed AUTHOR STATUS approved

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Last modified September 23 12:53 EDT 2020. Contains 337310 sequences. (Running on oeis4.)