login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A059529 For 1 < x, each c(i) is "multiply" (*) or "divide" (/); a(n) is number of choices for c(0),...,c(n-1) so that 1 c(0) x^1 c(1) x^2,.., c(n-1) x^n is an integer. 10
1, 1, 2, 5, 9, 16, 32, 68, 135, 256, 512, 1059, 2110, 4096, 8192, 16745, 33425, 65536, 131072, 266254, 531924, 1048576, 2097152, 4244214, 8482454, 16777216, 33554432, 67741466, 135417620, 268435456, 536870912, 1082015434, 2163280087, 4294967296, 8589934592 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

From Gus Wiseman, Jul 04 2019: (Start)

Also the number of subsets of {1..n} whose sum is less than or equal to the sum of their complement. For example, the a(0) = 1 through a(5) = 16 subsets are:

  {}  {}  {}   {}     {}     {}

          {1}  {1}    {1}    {1}

               {2}    {2}    {2}

               {3}    {3}    {3}

               {1,2}  {4}    {4}

                      {1,2}  {5}

                      {1,3}  {1,2}

                      {1,4}  {1,3}

                      {2,3}  {1,4}

                             {1,5}

                             {2,3}

                             {2,4}

                             {2,5}

                             {3,4}

                             {1,2,3}

                             {1,2,4}

(End)

LINKS

Table of n, a(n) for n=0..34.

FORMULA

a(0)=1; for 0<n, a(n) = A058377(n)+2^(n-1).

EXAMPLE

x = 3: for n = 2 there are 2 possibilities: 1*3*9=27 and 1/3*9=3. For n = 4 there are 9 possibilities: 1*3*9*27*81 1/3*9*27*81 1*3/9*27*81 1/3/9*27*81 1*3*9/27*81 1*3*9*27/81 1/3*9/27*81 1/3*9*27/81 1*3/9/27*81

MATHEMATICA

Table[Length[Select[Subsets[Range[n]], Plus@@Complement[Range[n], #]>=Plus@@#&]], {n, 0, 10}] (* Gus Wiseman, Jul 04 2019 *)

CROSSREFS

Cf. A058524, A058377.

Cf. A053632, A063865, A326173, A326174, A326175.

Sequence in context: A290464 A039946 A130752 * A271318 A119676 A036711

Adjacent sequences:  A059526 A059527 A059528 * A059530 A059531 A059532

KEYWORD

nonn

AUTHOR

Naohiro Nomoto, Feb 16 2001

EXTENSIONS

More terms from Alois P. Heinz, Jun 13 2019

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified July 23 03:00 EDT 2019. Contains 325230 sequences. (Running on oeis4.)