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A326439
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Number of maximal subsets of {1..n} such that no two elements have the same sorted prime signature.
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5
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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
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OFFSET
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0,4
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COMMENTS
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The sorted prime signature (A118914) of a positive integer is the multiset of exponents in its standard factorization into prime numbers.
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LINKS
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Andrew Howroyd, Table of n, a(n) for n = 0..1000
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EXAMPLE
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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}
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MATHEMATICA
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prisig[n_]:=If[n==1, {}, Sort[Last/@FactorInteger[n]]];
Table[Times@@(Length/@Split[Sort[Array[prisig, n]]]), {n, 0, 30}]
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PROG
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(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
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CROSSREFS
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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
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KEYWORD
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nonn
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AUTHOR
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Gus Wiseman, Jul 06 2019
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STATUS
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approved
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