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A337256
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Number of strict chains of divisors of n.
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13
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2, 4, 4, 8, 4, 12, 4, 16, 8, 12, 4, 32, 4, 12, 12, 32, 4, 32, 4, 32, 12, 12, 4, 80, 8, 12, 16, 32, 4, 52, 4, 64, 12, 12, 12, 104, 4, 12, 12, 80, 4, 52, 4, 32, 32, 12, 4, 192, 8, 32, 12, 32, 4, 80, 12, 80, 12, 12, 4, 176, 4, 12, 32, 128, 12, 52, 4, 32, 12, 52
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OFFSET
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1,1
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LINKS
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FORMULA
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EXAMPLE
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The a(n) chains for n = 1, 2, 4, 6, 8 (empty chains shown as 0):
0 0 0 0 0
1 1 1 1 1
2 2 2 2
2/1 4 3 4
2/1 6 8
4/1 2/1 2/1
4/2 3/1 4/1
4/2/1 6/1 4/2
6/2 8/1
6/3 8/2
6/2/1 8/4
6/3/1 4/2/1
8/2/1
8/4/1
8/4/2
8/4/2/1
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MATHEMATICA
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stableSets[u_, Q_]:=If[Length[u]==0, {{}}, With[{w=First[u]}, Join[stableSets[DeleteCases[u, w], Q], Prepend[#, w]&/@stableSets[DeleteCases[u, r_/; r==w||Q[r, w]||Q[w, r]], Q]]]];
Table[Length[stableSets[Divisors[n], !(Divisible[#1, #2]||Divisible[#2, #1])&]], {n, 10}]
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CROSSREFS
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A067824 is the case of chains starting with n (or ending with 1).
A074206 is the case of chains from n to 1.
A001222 counts prime factors with multiplicity.
A074206 counts chains of divisors from n to 1.
A122651 counts chains of divisors summing to n.
A167865 counts chains of divisors > 1 summing to n.
A334996 appears to count chains of divisors from n to 1 by length.
A337071 counts chains of divisors starting with n!.
A337255 counts chains of divisors starting with n by length.
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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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