A348605 - OEIS

%I #11 Oct 26 2021 04:27:34

%S 8505,10395,12285,15015,16065,17955,19635,21735,21945,23205,25515,

%T 25935,26565,28875,31185,31395,33495,33915,34125,35805,36855,39585,

%U 41055,42315,42735,45885,47355,48195,49665,50505,51765,53865,54285,55965,56595,58695,61215,64155

%N Odd nonexponential abundant numbers: odd numbers k such that A160135(k) > k.

%C The odd terms of A348604.

%C The numbers of terms not exceeding 10^k, for k = 4, 5, ..., are 1, 51, 360, 4117, 39803, 418663, 4099004, ... Apparently this sequence has an asymptotic density 0.0004...

%H Amiram Eldar, <a href="/A348605/b348605.txt">Table of n, a(n) for n = 1..10000</a>

%e 8505 is a term since A160135(8505) = 8862 > 8505.

%t esigma[n_] := Times @@ (Sum[First[#]^d, {d, Divisors[Last[#]]}] &) /@ FactorInteger[n]; q[n_] := DivisorSigma[1, n] - esigma[n] > n; Select[Range[1, 65000, 2], q]

%Y Cf. A160135.

%Y Subsequence of A005231 and A348604.

%Y Similar sequences: A094889, A127666, A129485, A293186, A321147, A348275.

%K nonn

%O 1,1

%A _Amiram Eldar_, Oct 25 2021