A025610 Numbers of form 2^i*6^j, with i, j >= 0; equivalently, numbers of the form 2^i*3^j with 0 <= j <= i.

1, 2, 4, 6, 8, 12, 16, 24, 32, 36, 48, 64, 72, 96, 128, 144, 192, 216, 256, 288, 384, 432, 512, 576, 768, 864, 1024, 1152, 1296, 1536, 1728, 2048, 2304, 2592, 3072, 3456, 4096, 4608, 5184, 6144, 6912, 7776, 8192, 9216, 10368, 12288, 13824, 15552, 16384, 18432

Offset: 1

Author

David W. Wilson

Keywords

• easy
• nonn

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Crossrefs

Intersection of A025487 and A003586.

Programs

Mathematica

n = 10^6; Flatten[Table[2^i*6^j, {i, 0, Log2[n]}, {j, 0, Log[6, n/2^i]}]] // Sort (* Amiram Eldar, Sep 26 2020 *)

PARI

list(lim)=my(v=List(),t); for(j=0,logint(lim\=1,6), t=6^j; while(t<=lim, listput(v,t); t<<=1)); Set(v) \\ Charles R Greathouse IV, Dec 14 2016

Formula

From Vaclav Kotesovec, Sep 25 2020: (Start)

a(n) ~ exp(sqrt(2*log(2)*log(6)*n)) / sqrt(12).

Sum_{k>=1} 1/a(k) = 12/5. (End)

a(n) = 2^A025636(n) * 6^A025656(n). - R. J. Mathar, Jul 06 2025