A025620 Numbers of the form 4^i * 9^j, with i, j >= 0.

1, 4, 9, 16, 36, 64, 81, 144, 256, 324, 576, 729, 1024, 1296, 2304, 2916, 4096, 5184, 6561, 9216, 11664, 16384, 20736, 26244, 36864, 46656, 59049, 65536, 82944, 104976, 147456, 186624, 236196, 262144, 331776, 419904, 531441, 589824, 746496, 944784

Offset: 1

Author

David W. Wilson

Keywords

• easy
• nonn

Comments

Numbers of the form 2^(2*i) * 3^(2*j) or 3-smooth squares: intersection of A003586 and A000290; A001221(a(n)) <= 2; A001222(a(n)) is even; A006530(a(n)) <= 3. - Reinhard Zumkeller, May 16 2015

Closed under multiplication. - Klaus Purath, Oct 06 2023

Links

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

Crossrefs

Cf. A003586, A000290, A001221, A001222, A006530, subsequence of A036667.

Cf. A022328, A022329.

Programs

Haskell

import Data.Set (singleton, deleteFindMin, insert)
a025620 n = a025620_list !! (n-1)
a025620_list = f $ singleton 1 where
   f s = y : f (insert (4 * y) $ insert (9 * y) s')
               where (y, s') = deleteFindMin s
-- Reinhard Zumkeller, May 16 2015

Mathematica

n = 10^6; Flatten[Table[4^i*9^j, {i, 0, Log[4, n]}, {j, 0, Log[9, n/4^i]}]] // Sort (* Amiram Eldar, Sep 24 2020 *)

PARI

list(lim)=my(v=List(), N); for(n=0, logint(lim\=1, 9), N=9^n; while(N<=lim, listput(v, N); N<<=2)); Set(v) \\ Charles R Greathouse IV, Jan 10 2018

Formula

Sum_{n>=1} 1/a(n) = (4*9)/((4-1)*(9-1)) = 3/2. - Amiram Eldar, Sep 24 2020

a(n) ~ exp(sqrt(8*log(2)*log(3)*n)) / 6 . - Vaclav Kotesovec, Sep 24 2020

a(n) = A003586(n)^2 = 4^A022328(n) * 9^A022329(n). - R. J. Mathar, Jul 06 2025