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A328195
Maximum length of a divisibility chain of consecutive divisors of n greater than 1.
8
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
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).
Sequence in context: A304465 A304687 A076558 * A235875 A328026 A326975
KEYWORD
nonn
AUTHOR
Gus Wiseman, Oct 14 2019
EXTENSIONS
Data section extended up to a(105) by Antti Karttunen, Dec 07 2024
STATUS
approved