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 A077567 Least k >= 2 such that sigma(n) divides sigma(n^k). 1
 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, 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, 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS From Robert Israel, Mar 14 2017: (Start) If x and y are coprime and a(x)=a(y)=k, then a(xy)=k as well. If n > 1 is squarefree, then a(n^k) = k+2 for all k>=1. Is there any n > 1 with a(n) = 2? (End) LINKS Robert Israel, Table of n, a(n) for n = 1..10000 MAPLE f:= proc(n) local k, s; uses numtheory;   s:= sigma(n);   for k from 2 do if sigma(n^k) mod s = 0 then return k fi   od end proc: map(f, [\$1..200]); # Robert Israel, Mar 14 2017 MATHEMATICA a[n_] := For[k = 2, True, k++, If[Divisible[DivisorSigma[1, n^k], DivisorSigma[1, n]], Return[k]]]; Array[a, 100] (* Jean-François Alcover, Aug 24 2020 *) CROSSREFS Sequence in context: A139069 A071866 A077603 * A096344 A030349 A285203 Adjacent sequences:  A077564 A077565 A077566 * A077568 A077569 A077570 KEYWORD nonn AUTHOR Benoit Cloitre, Dec 01 2002 STATUS approved

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Last modified September 18 03:35 EDT 2020. Contains 337164 sequences. (Running on oeis4.)