

A328195


Maximum length of a divisibility chain of consecutive divisors of n greater than 1.


5



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

1,4


COMMENTS

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.


LINKS

Table of n, a(n) for n=1..87.


EXAMPLE

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.


MATHEMATICA

Table[If[n==1, 0, Max@@Length/@Split[DeleteCases[Divisors[n], 1], Divisible[#2, #1]&]], {n, 100}]


CROSSREFS

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 runlength 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


KEYWORD

nonn


AUTHOR

Gus Wiseman, Oct 14 2019


STATUS

approved



