A326438 Number of subsets of {1..n} such that no two elements have the same sorted prime signature.

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

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