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A326439 Number of maximal subsets of {1..n} such that no two elements have the same sorted prime signature. 5
1, 1, 1, 2, 2, 3, 3, 4, 4, 8, 16, 20, 20, 24, 36, 48, 48, 56, 112, 128, 192, 240, 288, 324, 324, 486, 567, 1134, 1512, 1680, 1680, 1848, 1848, 2112, 2376, 2640, 2640, 2880, 3168, 3456, 6912, 7488, 14976, 16128, 20160, 24192, 26208, 28080, 28080, 37440, 43680 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

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

LINKS

Andrew Howroyd, Table of n, a(n) for n = 0..1000

EXAMPLE

The a(0) = 1 through a(9) = 8 subsets:

  {}  {1}  {12}  {12}  {124}  {124}  {1246}  {1246}  {12468}  {12468}

                 {13}  {134}  {134}  {1346}  {1346}  {13468}  {12689}

                              {145}  {1456}  {1456}  {14568}  {13468}

                                             {1467}  {14678}  {13689}

                                                              {14568}

                                                              {14678}

                                                              {15689}

                                                              {16789}

MATHEMATICA

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

Table[Times@@(Length/@Split[Sort[Array[prisig, n]]]), {n, 0, 30}]

PROG

(PARI) a(n)={if(n==0, 1, my(M=Map()); for(i=1, n, my(f=factor(i)[, 2], s=sum(k=1, #f, x^f[k]), z); mapput(M, s, if(mapisdefined(M, s, &z), z + 1, 1))); vecprod(Mat(M)[, 2]))} \\ Andrew Howroyd, Aug 30 2019

CROSSREFS

Cf. A001221, A001222, A025487, A064839, A085089, A112798, A118914, A124010, A181819, A324762, A325263, A325365, A326438, A326441.

Sequence in context: A318296 A035679 A337587 * A136537 A153928 A119446

Adjacent sequences:  A326436 A326437 A326438 * A326440 A326441 A326442

KEYWORD

nonn

AUTHOR

Gus Wiseman, Jul 06 2019

STATUS

approved

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Last modified August 16 21:38 EDT 2022. Contains 356169 sequences. (Running on oeis4.)