cp's OEIS Frontend

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

%I A025620 #40 Jul 06 2025 11:25:14
%S A025620 1,4,9,16,36,64,81,144,256,324,576,729,1024,1296,2304,2916,4096,5184,
%T A025620 6561,9216,11664,16384,20736,26244,36864,46656,59049,65536,82944,
%U A025620 104976,147456,186624,236196,262144,331776,419904,531441,589824,746496,944784
%N A025620 Numbers of the form 4^i * 9^j, with i, j >= 0.
%C A025620 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
%C A025620 Closed under multiplication. - _Klaus Purath_, Oct 06 2023
%H A025620 Reinhard Zumkeller, <a href="/A025620/b025620.txt">Table of n, a(n) for n = 1..10000</a>
%F A025620 Sum_{n>=1} 1/a(n) = (4*9)/((4-1)*(9-1)) = 3/2. - _Amiram Eldar_, Sep 24 2020
%F A025620 a(n) ~ exp(sqrt(8*log(2)*log(3)*n)) / 6 . - _Vaclav Kotesovec_, Sep 24 2020
%F A025620 a(n) = A003586(n)^2 = 4^A022328(n) * 9^A022329(n). - _R. J. Mathar_, Jul 06 2025
%t A025620 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 *)
%o A025620 (Haskell)
%o A025620 import Data.Set (singleton, deleteFindMin, insert)
%o A025620 a025620 n = a025620_list !! (n-1)
%o A025620 a025620_list = f $ singleton 1 where
%o A025620    f s = y : f (insert (4 * y) $ insert (9 * y) s')
%o A025620                where (y, s') = deleteFindMin s
%o A025620 -- _Reinhard Zumkeller_, May 16 2015
%o A025620 (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
%Y A025620 Cf. A003586, A000290, A001221, A001222, A006530, subsequence of A036667.
%Y A025620 Cf. A022328, A022329.
%K A025620 easy,nonn
%O A025620 1,2
%A A025620 _David W. Wilson_