cp's OEIS Frontend

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

%I A328162 #8 Apr 20 2023 02:11:15
%S A328162 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,
%T A328162 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,
%U A328162 2,2,2,2,2,2,2,3,2,2,2,3,5,2,2,2,2,2,2
%N A328162 Maximum length of a divisibility chain of consecutive divisors of n.
%H A328162 Robert Israel, <a href="/A328162/b328162.txt">Table of n, a(n) for n = 1..10000</a>
%e A328162 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.
%p A328162 f:= proc(n) local F,L,d,i;
%p A328162   F:= sort(convert(numtheory:-divisors(n),list));
%p A328162   d:= nops(F);
%p A328162   L:= Vector(d);
%p A328162   L[1]:= 1;
%p A328162   for i from 2 to d do
%p A328162     if F[i] mod F[i-1] = 0 then L[i]:= L[i-1]+1
%p A328162     else L[i]:= 1
%p A328162     fi
%p A328162   od;
%p A328162   max(L)
%p A328162 end proc:
%p A328162 map(f, [$1..100]); # _Robert Israel_, Apr 20 2023
%t A328162 Table[Max@@Length/@Split[Divisors[n],Divisible[#2,#1]&],{n,100}]
%Y A328162 Records occur at powers of 2 (A000079).
%Y A328162 Taking only proper divisors gives A328194.
%Y A328162 Taking only divisors > 1 gives A328195.
%Y A328162 The maximum run-length among divisors of n is A055874.
%Y A328162 Cf. A000005, A027750, A060680, A060775, A328026, A328028, A328161, A328189.
%K A328162 nonn
%O A328162 1,2
%A A328162 _Gus Wiseman_, Oct 06 2019