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A337072
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Number of factorizations of the superprimorial A006939(n) into squarefree numbers > 1.
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4
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1, 1, 2, 10, 141, 6769, 1298995, 1148840085, 5307091649182, 143026276277298216, 24801104674619158730662, 30190572492693121799801655311, 278937095127086600900558327826721594
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OFFSET
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0,3
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COMMENTS
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The n-th superprimorial is A006939(n) = Product_{i = 1..n} prime(i)^(n - i + 1), which has n! divisors.
Also the number of set multipartitions (multisets of sets) of the multiset of prime factors of the superprimorial A006939(n).
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LINKS
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FORMULA
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EXAMPLE
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The a(1) = 1 through a(3) = 10 factorizations:
2 2*6 2*6*30
2*2*3 6*6*10
2*5*6*6
2*2*3*30
2*2*6*15
2*3*6*10
2*2*3*5*6
2*2*2*3*15
2*2*3*3*10
2*2*2*3*3*5
The a(1) = 1 through a(3) = 10 set multipartitions:
{1} {1}{12} {1}{12}{123}
{1}{1}{2} {12}{12}{13}
{1}{1}{12}{23}
{1}{1}{2}{123}
{1}{2}{12}{13}
{1}{3}{12}{12}
{1}{1}{1}{2}{23}
{1}{1}{2}{2}{13}
{1}{1}{2}{3}{12}
{1}{1}{1}{2}{2}{3}
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MATHEMATICA
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chern[n_]:=Product[Prime[i]^(n-i+1), {i, n}];
facsqf[n_]:=If[n<=1, {{}}, Join@@Table[Map[Prepend[#, d]&, Select[facsqf[n/d], Min@@#>=d&]], {d, Select[Rest[Divisors[n]], SquareFreeQ]}]];
Table[Length[facsqf[chern[n]]], {n, 0, 3}]
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PROG
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a(n) = {if(n==0, 1, count(vector(n, i, i)))} \\ Andrew Howroyd, Aug 31 2020
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CROSSREFS
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A000142 counts divisors of superprimorials.
A022915 counts permutations of the same multiset.
A103774 is the version for factorials instead of superprimorials.
A337073 is the strict case (strict factorizations into squarefree numbers).
A006939 lists superprimorials or Chernoff numbers.
A045778 counts strict factorizations.
A050320 counts factorizations into squarefree numbers.
A050326 counts strict factorizations into squarefree numbers.
A089259 counts set multipartitions of integer partitions.
A116540 counts normal set multipartitions.
A317829 counts factorizations of superprimorials.
A337069 counts strict factorizations of superprimorials.
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KEYWORD
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nonn,more
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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