cp's OEIS Frontend

A049605 Smallest k>1 such that k divides sigma(k*n).

%I A049605 #18 Jan 29 2023 18:52:52
%S A049605 6,3,2,6,2,2,2,3,6,2,2,2,2,2,2,6,2,3,2,2,2,2,2,2,6,2,2,2,2,2,2,3,2,2,
%T A049605 2,6,2,2,2,2,2,2,2,2,2,2,2,2,3,3,2,2,2,2,2,2,2,2,2,2,2,2,2,6,2,2,2,2,
%U A049605 2,2,2,3,2,2,2,2,2,2,2,2,6,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,2,6,2,2,2,2,2
%N A049605 Smallest k>1 such that k divides sigma(k*n).
%C A049605 a(n) = 2, 3 or 6. For any m, a(A028983(m)) = 2. If a(m)=6 then m is a square but if m is a square a(m) is not necessarily 6, first example is 7: a(7^2)=3 (cf. A072864).
%H A049605 R. J. Mathar, <a href="/A049605/b049605.txt">Table of n, a(n) for n = 1..1000</a>
%p A049605 A049605 := proc(n)
%p A049605     for k from 2 do
%p A049605         if modp(numtheory[sigma](k*n),k) = 0 then
%p A049605             return k;
%p A049605         end if;
%p A049605     end do:
%p A049605 end proc: # _R. J. Mathar_, Oct 26 2015
%t A049605 sk[n_]:=Module[{k=2},While[!Divisible[DivisorSigma[1,k*n],k],k++];k]; sk /@ Range[110] (* _Harvey P. Dale_, Jan 04 2015 *)
%o A049605 (PARI) a(n) = {k = 2; while(sigma(k*n) % k, k++); k ;} \\ _Michel Marcus_, Nov 21 2013
%Y A049605 Cf. A028983 (locations of 2), A067051 (locations of 3), A072862 (locations of 6).
%K A049605 easy,nonn
%O A049605 1,1
%A A049605 _Benoit Cloitre_, Jul 26 2002