A326439 - OEIS

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A326439

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

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