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A325263 Number of subsets of {1..n} containing n such that no two elements have the same sorted prime signature. 4
1, 2, 2, 6, 4, 16, 8, 40, 40, 60, 36, 216, 72, 168, 168, 840, 240, 960, 360, 1080, 864, 864, 672, 6720, 4480, 2560, 10240, 7680, 3840, 42240, 7680, 92160, 23040, 23040, 23040, 253440, 42240, 49920, 49920, 324480, 74880, 524160, 112320, 336960, 336960, 181440 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

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=1..46.

FORMULA

a(n) = A326438(n)/(1 + A064839(n)).

EXAMPLE

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

  {1}  {2}    {3}    {4}      {5}      {6}        {7}

       {1,2}  {1,3}  {1,4}    {1,5}    {1,6}      {1,7}

                     {2,4}    {4,5}    {2,6}      {4,7}

                     {3,4}    {1,4,5}  {3,6}      {6,7}

                     {1,2,4}           {4,6}      {1,4,7}

                     {1,3,4}           {5,6}      {1,6,7}

                                       {1,2,6}    {4,6,7}

                                       {1,3,6}    {1,4,6,7}

                                       {1,4,6}

                                       {1,5,6}

                                       {2,4,6}

                                       {3,4,6}

                                       {4,5,6}

                                       {1,2,4,6}

                                       {1,3,4,6}

                                       {1,4,5,6}

MATHEMATICA

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

Table[Times@@(1+Length/@Split[Sort[Array[prisig, n]]])/(1+Count[Array[prisig, n], prisig[n]]), {n, 30}]

CROSSREFS

Cf. A001221, A001222, A025487, A064839, A085089, A112798, A118914, A124010, A181819, A325365, A326438, A326439, A326441.

Sequence in context: A100495 A056463 A309694 * A005992 A085050 A329249

Adjacent sequences:  A325260 A325261 A325262 * A325264 A325265 A325266

KEYWORD

nonn

AUTHOR

Gus Wiseman, Jul 06 2019

STATUS

approved

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Last modified September 17 06:16 EDT 2021. Contains 347478 sequences. (Running on oeis4.)