login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A326438 Number of subsets of {1..n} such that no two elements have the same sorted prime signature. 4
1, 2, 4, 6, 12, 16, 32, 40, 80, 120, 180, 216, 432, 504, 672, 840, 1680, 1920, 2880, 3240, 4320, 5184, 6048, 6720, 13440, 17920, 20480, 30720, 38400, 42240, 84480, 92160, 184320, 207360, 230400, 253440, 506880, 549120, 599040, 648960, 973440 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

The sorted prime signature (A118914) of a positive integer is the multiset of exponents in its standard factorization into prime numbers.

LINKS

Table of n, a(n) for n=0..40.

EXAMPLE

The a(0) = 1 through a(5) = 16 subsets:

  {}  {}   {}     {}     {}       {}

      {1}  {1}    {1}    {1}      {1}

           {2}    {2}    {2}      {2}

           {1,2}  {3}    {3}      {3}

                  {1,2}  {4}      {4}

                  {1,3}  {1,2}    {5}

                         {1,3}    {1,2}

                         {1,4}    {1,3}

                         {2,4}    {1,4}

                         {3,4}    {1,5}

                         {1,2,4}  {2,4}

                         {1,3,4}  {3,4}

                                  {4,5}

                                  {1,2,4}

                                  {1,3,4}

                                  {1,4,5}

MATHEMATICA

prisig[n_]:=If[n==1, {}, Sort[Last/@FactorInteger[n]]];

Table[Length[Select[Subsets[Range[n]], UnsameQ@@prisig/@#&]], {n, 0, 10}]

CROSSREFS

Cf. A001221, A001222, A025487, A064839, A085089, A112798, A118914, A124010, A181819, A325263, A325365, A326439, A326441.

Sequence in context: A284456 A233968 A120453 * A023995 A018189 A239954

Adjacent sequences:  A326435 A326436 A326437 * A326439 A326440 A326441

KEYWORD

nonn

AUTHOR

Gus Wiseman, Jul 06 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 | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified August 9 21:08 EDT 2022. Contains 356026 sequences. (Running on oeis4.)