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A054030 Sigma(n)/n for n such that sigma(n) is divisible by n.

%I A054030 #29 Feb 16 2025 08:32:42
%S A054030 1,2,2,3,2,3,2,4,4,3,4,4,2,4,4,3,4,3,2,5,5,4,3,4,2,4,4,5,4,5,5,4,5,5,
%T A054030 4,4,4,5,4,4,2,5,4,5,6,5,5,5,5,5,5,6,5,5,4,5,6,5,4,4,5,4,5,4,6,6,6,6,
%U A054030 6,6,6,6,5,6,6,5,6,5,6,6,5,4,4,5,4,4,5,6,5,5,4,6,4,4,6,5,6,6,6,6,6,6,6,5,6
%N A054030 Sigma(n)/n for n such that sigma(n) is divisible by n.
%C A054030 The graph supports the conjecture that all numbers except 2 appear only a finite number of times. Sequences A000396, A005820, A027687, A046060 and A046061 give the n for which the abundancy sigma(n)/n is 2, 3, 4, 5 and 6, respectively. See A134639 for the number of n having abundancy greater than 2. - _T. D. Noe_, Nov 04 2007
%H A054030 T. D. Noe, <a href="/A054030/b054030.txt">Table of n, a(n) for n = 1..1600</a> (using Flammenkamp's data)
%H A054030 Achim Flammenkamp, <a href="http://wwwhomes.uni-bielefeld.de/achim/mpn.html">The Multiply Perfect Numbers Page</a>
%H A054030 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Abundancy.html">Abundancy</a>
%F A054030 a(n) = sigma(A007691(n))/A007691(n)
%p A054030 with(numtheory): for i while i < 33000 do
%p A054030 if sigma(i) mod i = 0 then print(sigma(i)/i) fi od;
%o A054030 (PARI) for(n=1,1e7,if(denominator(k=sigma(n,-1))==1, print1(k", "))) \\ _Charles R Greathouse IV_, Mar 09 2014
%Y A054030 Cf. A000203, A007691, A054024, A065997, A219545.
%K A054030 nonn,easy
%O A054030 1,2
%A A054030 _Asher Auel_, Jan 19 2000
%E A054030 More terms from _Jud McCranie_, Jul 09 2000
%E A054030 More terms from _David Wasserman_, Jun 28 2004