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A337105
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Number of strict chains of divisors from n! to 1.
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19
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1, 1, 1, 3, 20, 132, 1888, 20128, 584000, 17102016, 553895936, 11616690176, 743337949184, 19467186157568, 999551845713920, 66437400489711616, 10253161206302064640, 388089999627661557760, 53727789519052432998400, 2325767421950553303285760, 365546030278816140131041280
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OFFSET
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0,4
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LINKS
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FORMULA
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EXAMPLE
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The a(4) = 20 chains:
24/1 24/2/1 24/4/2/1 24/8/4/2/1
24/3/1 24/6/2/1 24/12/4/2/1
24/4/1 24/6/3/1 24/12/6/2/1
24/6/1 24/8/2/1 24/12/6/3/1
24/8/1 24/8/4/1
24/12/1 24/12/2/1
24/12/3/1
24/12/4/1
24/12/6/1
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MAPLE
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b:= proc(n) option remember; 1 +
add(b(d), d=numtheory[divisors](n) minus {n})
end:
a:= n-> ceil(b(n!)/2):
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MATHEMATICA
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chnsc[n_]:=Prepend[Join@@Table[Prepend[#, n]&/@chnsc[d], {d, DeleteCases[Divisors[n], 1|n]}], {n}];
Table[Length[chnsc[n!]], {n, 0, 5}]
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CROSSREFS
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A336941 is the version for superprimorials.
A337104 counts the case with distinct prime multiplicities.
A337071 is the case not necessarily ending with 1.
A027423 counts divisors of factorial numbers.
A067824 counts chains of divisors starting with n.
A074206 counts chains of divisors from n to 1.
A076716 counts factorizations of factorial numbers.
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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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