A328195 Maximum length of a divisibility chain of consecutive divisors of n greater than 1.

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, 4, 1, 2, 2, 3, 2, 2, 2, 2, 1, 2, 3, 3, 1, 2, 1, 4, 2

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

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

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}]

Prog

(PARI) A328195(n) = if(1==n, 0, my(divs=divisors(n), rl=0, ml=1); for(i=2, #divs, if(!(divs[i]%divs[i-1]), rl++, ml = max(rl, ml); rl=1)); max(ml, rl)); \\ Antti Karttunen, Dec 07 2024

Crossrefs

Allowing 1 as a divisor gives A328162.

Forbidding n as a divisor of n gives A328194.

Positions of 1's are A000040 (primes).

Indices of terms greater than 1 are A002808 (composite numbers).

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

Keyword

nonn

Author

Gus Wiseman, Oct 14 2019

Extensions

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

Status

approved