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A337073
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Number of strict factorizations of the superprimorial A006939(n) into squarefree numbers > 1.
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3
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1, 1, 1, 2, 14, 422, 59433, 43181280, 178025660042, 4550598470020490, 782250333882971717562, 974196106965358319940100513, 9412280190038329162111356578977100, 751537739224674099813783040471383322758327
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OFFSET
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0,4
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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). It has n! divisors.
Also the number of strict set multipartitions (sets 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*6*30*210
2*3*6*10 6*10*30*42
2*3*6*30*70
2*5*6*30*42
2*3*10*30*42
2*3*6*10*210
2*6*10*15*42
2*6*10*21*30
2*6*14*15*30
3*6*10*14*30
2*3*5*6*10*42
2*3*5*6*14*30
2*3*6*7*10*30
2*3*6*10*14*15
The a(1) = 1 through a(3) = 14 set multipartitions:
{1} {1}{12} {1}{12}{123} {1}{12}{123}{1234}
{1}{2}{12}{13} {12}{13}{123}{124}
{1}{12}{13}{23}{124}
{1}{12}{13}{24}{123}
{1}{12}{14}{23}{123}
{1}{2}{12}{123}{134}
{1}{2}{12}{13}{1234}
{1}{2}{13}{123}{124}
{1}{3}{12}{123}{124}
{2}{12}{13}{14}{123}
{1}{2}{12}{13}{14}{23}
{1}{2}{12}{4}{13}{123}
{1}{2}{3}{12}{13}{124}
{1}{2}{3}{12}{14}{123}
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MATHEMATICA
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chern[n_]:=Product[Prime[i]^(n-i+1), {i, n}];
ystfac[n_]:=If[n<=1, {{}}, Join@@Table[Map[Prepend[#, d]&, Select[ystfac[n/d], Min@@#>d&]], {d, Select[Rest[Divisors[n]], SquareFreeQ]}]];
Table[Length[ystfac[chern[n]]], {n, 0, 4}]
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PROG
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a(n) = {if(n==0, 1, count(vector(n, i, i)))} \\ Andrew Howroyd, Sep 01 2020
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CROSSREFS
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A000142 counts divisors of superprimorials.
A022915 counts permutations of the same multiset.
A103775 is the version for factorials instead of superprimorials.
A006939 lists superprimorials or Chernoff numbers.
A045778 counts strict factorizations.
A050320 counts factorizations into squarefree numbers.
A050326 counts strict factorizations into squarefree numbers.
A050342 counts strict set multipartitions of integer partitions.
A283877 counts non-isomorphic strict 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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