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%I #11 Oct 09 2022 04:22:46
%S 4725,6615,7875,8505,11025,14175,15435,17325,19845,20475,22275,23625,
%T 24255,25515,26775,28665,29925,31185,33075,36225,36855,37125,37485,
%U 38115,39375,40425,41895,42525,46305,47775,48195,50715,51975,53235,53865,55125,57915,59535
%N Odd numbers k such that A162296(k) > 2*k.
%C The least term that is not divisible by 3 is a(89047132) = 134785275625.
%C The numbers of terms not exceeding 10^k, for k = 4, 5, ..., are 4, 60, 640, 6650, 66044, 660230, 6604594, 66073470, ... . Apparently, the asymptotic density of this sequence exists and equals 0.000660... .
%H Amiram Eldar, <a href="/A357607/b357607.txt">Table of n, a(n) for n = 1..10000</a>
%e 4725 is a term since it is odd, and A162296(4725) = 9728 > 2*4725.
%t q[n_] := Module[{f = FactorInteger[n], p, e}, p = f[[;; , 1]]; e = f[[;; , 2]]; Times @@ ((p^(e + 1) - 1)/(p - 1)) - Times @@ (p + 1) > 2*n]; Select[Range[3, 60000, 2], q]
%Y Cf. A162296.
%Y Subsequence of A005231, A013929 and A357605.
%Y Similar sequences: A094889, A127666, A129485, A293186, A321147, A348275, A348605.
%K nonn
%O 1,1
%A _Amiram Eldar_, Oct 06 2022
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