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A337069
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Number of strict factorizations of the superprimorial A006939(n).
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4
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1, 1, 3, 34, 1591, 360144, 442349835, 3255845551937, 156795416820025934, 53452979022001011490033, 138542156296245533221812350867, 2914321438328993304235584538307144802, 528454951438415221505169213611461783474874149, 873544754831735539240447436467067438924478174290477803
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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).
Also the number of strict multiset partitions of {1,2,2,3,3,3,...,n}, a multiset with i copies of i for i = 1..n.
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LINKS
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FORMULA
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EXAMPLE
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The a(3) = 34 factorizations:
2*3*4*15 2*3*60 2*180 360
2*3*5*12 2*4*45 3*120
2*3*6*10 2*5*36 4*90
2*4*5*9 2*6*30 5*72
3*4*5*6 2*9*20 6*60
2*10*18 8*45
2*12*15 9*40
3*4*30 10*36
3*5*24 12*30
3*6*20 15*24
3*8*15 18*20
3*10*12
4*5*18
4*6*15
4*9*10
5*6*12
5*8*9
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MATHEMATICA
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chern[n_]:=Product[Prime[i]^(n-i+1), {i, n}];
stfa[n_]:=If[n<=1, {{}}, Join@@Table[Map[Prepend[#, d]&, Select[stfa[n/d], Min@@#>d&]], {d, Rest[Divisors[n]]}]];
Table[Length[stfa[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, Sep 01 2020
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CROSSREFS
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A022915 counts permutations of the same multiset.
A157612 is the version for factorials instead of superprimorials.
A337072 is the non-strict version with squarefree factors.
A337073 is the case with squarefree factors.
A000217 counts prime factors (with multiplicity) of superprimorials.
A006939 lists superprimorials or Chernoff numbers.
A045778 counts strict factorizations.
A322583 counts factorizations into factorials.
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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