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A328195
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Maximum length of a divisibility chain of consecutive divisors of n greater than 1.
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5
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0, 1, 1, 2, 1, 2, 1, 3, 2, 2, 1, 2, 1, 2, 2, 4, 1, 2, 1, 3, 2, 2, 1, 2, 2, 2, 3, 3, 1, 2, 1, 5, 2, 2, 2, 2, 1, 2, 2, 3, 1, 2, 1, 3, 2, 2, 1, 2, 2, 2, 2, 3, 1, 2, 2, 3, 2, 2, 1, 2, 1, 2, 2, 6, 2, 2, 1, 3, 2, 2, 1, 2, 1, 2, 2, 3, 2, 2, 1, 3, 4, 2, 1, 2, 2, 2, 2
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OFFSET
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1,4
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COMMENTS
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Also the maximum length of a divisibility chain of consecutive divisors of n less than n.
The divisors of n (except 1) are row n of A027749.
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LINKS
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Table of n, a(n) for n=1..87.
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EXAMPLE
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The divisors of 272 greater than 1 are {2, 4, 8, 16, 17, 34, 68, 136, 272}, with divisibility chains {{2, 4, 8, 16}, {17, 34, 68, 136, 272}}, so a(272) = 5.
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MATHEMATICA
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Table[If[n==1, 0, Max@@Length/@Split[DeleteCases[Divisors[n], 1], Divisible[#2, #1]&]], {n, 100}]
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CROSSREFS
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Positions of 1's are A328028 without 1.
Allowing 1 as a divisor gives A328162.
Forbidding n as a divisor of n gives A328194.
Indices of terms greater than 1 are A328189.
The maximum run-length of divisors of n is A055874(n).
Cf. A000005, A033676, A060775, A163870, A328026, A328161, A328171.
Sequence in context: A304465 A304687 A076558 * A235875 A328026 A326975
Adjacent sequences: A328192 A328193 A328194 * A328196 A328197 A328198
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KEYWORD
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nonn
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AUTHOR
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Gus Wiseman, Oct 14 2019
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STATUS
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approved
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