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A336941
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Number of strict chains of divisors starting with the superprimorial A006939(n) and ending with 1.
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9
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1, 1, 8, 604, 691968, 16359233536, 10083474928244288, 195661337707783118840768, 139988400203593571474134024847360, 4231553868972506381329450624389969130848256, 6090860257621637852755610879241895108657182173073604608, 464479854191019594417264488167571483344961210693790188774166838214656
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OFFSET
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0,3
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LINKS
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FORMULA
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EXAMPLE
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The a(2) = 8 chains:
12/1
12/2/1
12/3/1
12/4/1
12/6/1
12/4/2/1
12/6/2/1
12/6/3/1
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MATHEMATICA
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chern[n_]:=Product[Prime[i]^(n-i+1), {i, n}];
chns[n_]:=If[n==1, 1, Sum[chns[d], {d, Most[Divisors[n]]}]];
Table[chns[chern[n]], {n, 0, 3}]
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PROG
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(PARI) a(n)={my(sig=vector(n, i, i), m=vecsum(sig)); sum(k=0, m, prod(i=1, #sig, binomial(sig[i]+k-1, k-1))*sum(r=k, m, binomial(r, k)*(-1)^(r-k)))} \\ Andrew Howroyd, Aug 30 2020
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CROSSREFS
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A336571 is the case with distinct prime multiplicities.
A074206 counts chains of divisors from n to 1.
A006939 lists superprimorials or Chernoff numbers.
A067824 counts divisor chains starting with n.
A317829 counts factorizations of superprimorials.
Cf. A000142, A001055, A002033, A008480, A022559, A027423, A124010, A167865, A181796, A336417, A336420, A337069.
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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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