A077567 - OEIS

%I #17 Aug 24 2020 10:44:43

%S 2,3,3,4,3,3,3,5,4,3,3,5,3,3,3,6,3,7,3,5,3,3,3,3,4,3,5,7,3,3,3,7,3,3,

%T 3,4,3,3,3,5,3,3,3,5,3,3,3,11,4,7,3,7,3,5,3,3,3,3,3,5,3,3,7,8,3,3,3,5,

%U 3,3,3,13,3,3,7,5,3,3,3,5,6,3,3,5,3,3,3,5,3,3,3,5,3,3,3,7,3,4,7,4,3,3,3

%N Least k >= 2 such that sigma(n) divides sigma(n^k).

%C From _Robert Israel_, Mar 14 2017: (Start)

%C If x and y are coprime and a(x)=a(y)=k, then a(xy)=k as well.

%C If n > 1 is squarefree, then a(n^k) = k+2 for all k>=1.

%C Is there any n > 1 with a(n) = 2? (End)

%H Robert Israel, <a href="/A077567/b077567.txt">Table of n, a(n) for n = 1..10000</a>

%p f:= proc(n) local k, s; uses numtheory;

%p   s:= sigma(n);

%p   for k from 2 do if sigma(n^k) mod s = 0 then return k fi

%p   od

%p end proc:

%p map(f, [$1..200]); # _Robert Israel_, Mar 14 2017

%t a[n_] := For[k = 2, True, k++, If[Divisible[DivisorSigma[1, n^k], DivisorSigma[1, n]], Return[k]]];

%t Array[a, 100] (* _Jean-François Alcover_, Aug 24 2020 *)

%K nonn

%O 1,1

%A _Benoit Cloitre_, Dec 01 2002