A328194 Maximum length of a divisibility chain of consecutive nontrivial divisors of n (greater than 1 and less than n).

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, 3, 0, 1, 1, 2, 1, 1, 1, 1, 0, 2, 2, 3, 0, 2, 0, 3, 1

Offset

1,8

Comments

The nontrivial divisors of n are row n of A163870.

Links

Antti Karttunen, Table of n, a(n) for n = 1..65537

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], 1|n], Divisible[#2, #1]&]], {n, 100}]

Prog

(PARI) A328194(n) = if(1==n || isprime(n), 0, my(divs=divisors(n), rl=0, ml=1); for(i=2, #divs-1, if(!(divs[i]%divs[i-1]), rl++, ml = max(rl, ml); rl=1)); max(ml, rl)); \\ Antti Karttunen, Dec 07 2024

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 run-length of divisors of n is A055874(n).

Cf. A000005, A033676, A060775, A163870, A328026, A328161, A328171.

Sequence in context: A156709 A081400 A378663 * A131963 A130538 A276007

Adjacent sequences: A328191 A328192 A328193 * A328195 A328196 A328197

Keyword

nonn

Author

Gus Wiseman, Oct 14 2019

Extensions

Data section extended up to a(105) by Antti Karttunen, Dec 07 2024

Status

approved