A328162 Maximum length of a divisibility chain of consecutive divisors of n.

1, 2, 2, 3, 2, 2, 2, 4, 3, 2, 2, 2, 2, 2, 2, 5, 2, 2, 2, 3, 2, 2, 2, 2, 3, 2, 4, 3, 2, 2, 2, 6, 2, 2, 2, 2, 2, 2, 2, 3, 2, 2, 2, 3, 2, 2, 2, 2, 3, 2, 2, 3, 2, 2, 2, 3, 2, 2, 2, 2, 2, 2, 2, 7, 2, 2, 2, 3, 2, 2, 2, 2, 2, 2, 2, 3, 2, 2, 2, 3, 5, 2, 2, 2, 2, 2, 2

Offset

1,2

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Example

The divisors of 968 split into consecutive divisibility chains {{1, 2, 4, 8}, {11, 22, 44, 88}, {121, 242, 484, 968}}, so a(968) = 4.

Maple

f:= proc(n) local F, L, d, i;
  F:= sort(convert(numtheory:-divisors(n), list));
  d:= nops(F);
  L:= Vector(d);
  L[1]:= 1;
  for i from 2 to d do
    if F[i] mod F[i-1] = 0 then L[i]:= L[i-1]+1
    else L[i]:= 1
    fi
  od;
  max(L)
end proc:
map(f, [$1..100]); # Robert Israel, Apr 20 2023

Mathematica

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

Crossrefs

Records occur at powers of 2 (A000079).

Taking only proper divisors gives A328194.

Taking only divisors > 1 gives A328195.

The maximum run-length among divisors of n is A055874.

Cf. A000005, A027750, A060680, A060775, A328026, A328028, A328161, A328189.

Sequence in context: A196229 A191302 A161189 * A067132 A336500 A328401

Adjacent sequences: A328159 A328160 A328161 * A328163 A328164 A328165

Keyword

nonn

Author

Gus Wiseman, Oct 06 2019

Status

approved