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A326438
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Number of subsets of {1..n} such that no two elements have the same sorted prime signature.
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4
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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
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OFFSET
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0,2
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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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Table of n, a(n) for n=0..40.
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EXAMPLE
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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}
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MATHEMATICA
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prisig[n_]:=If[n==1, {}, Sort[Last/@FactorInteger[n]]];
Table[Length[Select[Subsets[Range[n]], UnsameQ@@prisig/@#&]], {n, 0, 10}]
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CROSSREFS
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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
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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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