

A328194


Maximum length of a divisibility chain of consecutive nontrivial divisors of n (greater than 1 and less than n).


9



0, 0, 0, 1, 0, 1, 0, 2, 1, 1, 0, 1, 0, 1, 1, 3, 0, 2, 0, 2, 1, 1, 0, 1, 1, 1, 2, 2, 0, 1, 0, 4, 1, 1, 1, 1, 0, 1, 1, 2, 0, 2, 0, 2, 1, 1, 0, 1, 1, 2, 1, 2, 0, 2, 1, 2, 1, 1, 0, 1, 0, 1, 1, 5, 1, 2, 0, 2, 1, 1, 0, 1, 0, 1, 2, 2, 1, 2, 0, 2, 3, 1, 0, 1, 1, 1, 1
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OFFSET

1,8


COMMENTS

The nontrivial divisors of n are row n of A163870.


LINKS

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


EXAMPLE

The nontrivial divisors of 272 are {2, 4, 8, 16, 17, 34, 68, 136} with divisibility chains {{2, 4, 8, 16}, {17, 34, 68, 136}}, so a(272) = 4.


MATHEMATICA

Table[Switch[n, 1, 0, _?PrimeQ, 0, _, Max@@Length/@Split[DeleteCases[Divisors[n], 1n], Divisible[#2, #1]&]], {n, 100}]


CROSSREFS

Positions of 1's are A328028 without 1.
The version with all divisors allowed is A328162.
Allowing n as a divisor of n gives A328195.
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: A342595 A156709 A081400 * A131963 A130538 A276007
Adjacent sequences: A328191 A328192 A328193 * A328195 A328196 A328197


KEYWORD

nonn


AUTHOR

Gus Wiseman, Oct 14 2019


STATUS

approved



