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A337075
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Number of strict chains of divisors in A130091 (numbers with distinct prime multiplicities) starting with a proper divisor of n! and ending with 1.
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2
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1, 1, 1, 3, 14, 48, 384, 1308, 40288, 933848, 21077680, 75690016, 5471262080, 7964665440, 54595767744, 17948164982144, 3454946386353664, 5010658671663616, 723456523262697984, 950502767770273280, 165679731871366906880, 8443707247468681128448
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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(1) = 1 through a(4) = 14 chains (with n! prepended):
1 2/1 6/1 24/1
6/2/1 24/2/1
6/3/1 24/3/1
24/4/1
24/8/1
24/12/1
24/4/2/1
24/8/2/1
24/8/4/1
24/12/2/1
24/12/3/1
24/12/4/1
24/8/4/2/1
24/12/4/2/1
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MATHEMATICA
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chnstr[n_]:=If[n==1, 1, Sum[chnstr[d], {d, Select[Most[Divisors[n]], UnsameQ@@Last/@FactorInteger[#]&]}]];
Table[chnstr[n!], {n, 0, 5}]
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CROSSREFS
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A336571 is the generalization to not just factorial numbers.
A337104 is the version for chains containing n!.
A071625 counts distinct prime multiplicities.
A074206 counts chains of divisors from n to 1.
A130091 lists numbers with distinct prime multiplicities.
A181796 counts divisors with distinct prime multiplicities.
A327498 gives the maximum divisor with distinct prime multiplicities.
A336414 counts divisors of n! with distinct prime multiplicities.
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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