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A025620
Numbers of the form 4^i * 9^j, with i, j >= 0.
4
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
1,2
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
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
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 *)
PROG
(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
(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
CROSSREFS
Cf. A003586, A000290, A001221, A001222, A006530, subsequence of A036667.
Sequence in context: A256944 A349062 A106575 * A117218 A226076 A357753
KEYWORD
easy,nonn
STATUS
approved