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A318083 Numbers m such that sigma(sigma(m))/sigma(m) <= sigma(m)/m.

%I A318083 #15 Apr 04 2024 07:55:30
%S A318083 1,2,4,8,9,12,16,18,25,32,36,48,50,52,64,72,80,81,84,90,98,100,108,
%T A318083 112,128,144,150,156,162,180,192,196,200,208,225,240,242,244,252,256,
%U A318083 288,289,292,300,320,324,336,338,360,372,388,392,400,420,432,441,444,448,450,468,484
%N A318083 Numbers m such that sigma(sigma(m))/sigma(m) <= sigma(m)/m.
%C A318083 A318059 and A318060 give f(n) = sigma(sigma(n))/n.
%C A318083 Let g(n) = sigma(n)/n, then f(n) = g(sigma(n))*g(n).
%C A318083 For g(), see A017665 and A017666.
%C A318083 Then this sequence are the integers m for which g(sigma(m)) <= g(m).
%C A318083 Are there other integers than 1, for which sigma(sigma(m))/sigma(m) = sigma(m)/m?
%H A318083 Amiram Eldar, <a href="/A318083/b318083.txt">Table of n, a(n) for n = 1..10000</a>
%t A318083 q[n_] := Module[{s = DivisorSigma[1, n]}, DivisorSigma[1, s]/s <= s/n]; Select[Range[500], q] (* _Amiram Eldar_, Apr 04 2024 *)
%o A318083 (PARI) isok(n) = my(sn=sigma(n)); sigma(sn)/sn <= sn/n;
%Y A318083 Cf. A000203 (sigma), A017665, A017666, A051027, A318059, A318060, A318084.
%K A318083 nonn
%O A318083 1,2
%A A318083 _Michel Marcus_, Aug 15 2018