cp's OEIS Frontend

A067132 Number of elements in the largest set of divisors of n which are in geometric progression.

%I A067132 #24 Sep 13 2024 08:24:08
%S A067132 1,2,2,3,2,2,2,4,3,2,2,3,2,2,2,5,2,3,2,3,2,2,2,4,3,2,4,3,2,2,2,6,2,2,
%T A067132 2,3,2,2,2,4,2,2,2,3,3,2,2,5,3,3,2,3,2,4,2,4,2,2,2,3,2,2,3,7,2,2,2,3,
%U A067132 2,2,2,4,2,2,3,3,2,2,2,5,5,2,2,3,2,2,2,4,2,3,2,3,2,2,2,6,2,3,3,3,2,2,2
%N A067132 Number of elements in the largest set of divisors of n which are in geometric progression.
%C A067132 Also a(n) = minimal 'freeness' of n with regard to squares, cubes, etc: All entries where a(n) = 2 are squarefree (or prime); Entries where a(n) = 3 are cubefree (and thus free of higher powers) but not squarefree, and so on. - _Carl R. White_, Jul 27 2009
%C A067132 For n > 1, a(n) is asymptotic to A000005(n)/A001221(n). - _Eric Desbiaux_, Dec 10 2012
%H A067132 G. C. Greubel, <a href="/A067132/b067132.txt">Table of n, a(n) for n = 1..10000</a>
%F A067132 If the prime factorization of n>1 is p_1^e_1 ... p_k^e_k, then a(n) = 1+max(e_1, ..., e_k).
%F A067132 a(n) = A051903(n) + 1. - _Ridouane Oudra_, Sep 10 2024
%e A067132 a(12) = 3 as the divisors of 12 are {1,2,3,4,6,12} and the maximal subsets in geometric progression are {1,2,4} and {3,6,12}.
%e A067132 a(16) = 5; the maximal set is {1,2,4,8,16}.
%p A067132 seq(max(0,seq(padic[ordp](n, p), p in numtheory[factorset](n))) + 1, n=1..100); # _Ridouane Oudra_, Sep 10 2024
%t A067132 a[n_] := If[n==1, 1, Max@@Last/@FactorInteger[n]+1]
%Y A067132 Cf. A000961, A067131, A051903.
%K A067132 easy,nonn
%O A067132 1,2
%A A067132 _Amarnath Murthy_, Jan 09 2002
%E A067132 Edited by _Dean Hickerson_, Jan 15 2002