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A337074
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Number of strict chains of divisors in A130091 (numbers with distinct prime multiplicities), starting with n!.
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8
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1, 1, 2, 0, 28, 0, 768, 0, 0, 0, 42155360, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0
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OFFSET
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0,3
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COMMENTS
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Support appears to be {0, 1, 2, 4, 6, 10}.
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LINKS
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FORMULA
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EXAMPLE
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The a(4) = 28 chains:
24 24/1 24/2/1 24/4/2/1 24/8/4/2/1
24/2 24/3/1 24/8/2/1 24/12/4/2/1
24/3 24/4/1 24/8/4/1
24/4 24/4/2 24/8/4/2
24/8 24/8/1 24/12/2/1
24/12 24/8/2 24/12/3/1
24/8/4 24/12/4/1
24/12/1 24/12/4/2
24/12/2
24/12/3
24/12/4
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MATHEMATICA
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chnsc[n_]:=If[!UnsameQ@@Last/@FactorInteger[n], {}, If[n==1, {{1}}, Prepend[Join@@Table[Prepend[#, n]&/@chnsc[d], {d, Most[Divisors[n]]}], {n}]]];
Table[Length[chnsc[n!]], {n, 0, 6}]
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CROSSREFS
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A336867 is the complement of the support.
A336942 is half the version for superprimorials (n > 1).
A337071 does not require distinct prime multiplicities.
A337104 is the case of chains 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.
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.
A336415 counts divisors of n! with equal prime multiplicities.
Cf. A000110, A001055, A002033, A007489, A022559, A048656, A071626, A098859, A124010, A167865, A325617, A336416, A336424.
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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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