%I #10 Nov 13 2021 16:43:53
%S 126720,134400,149760,188160,195840,456960,510720,549120,618240,
%T 718080,748800,779520,802560,833280,940800,979200,994560,1094400,
%U 1102080,1155840,1263360,1324800,1393920,1424640,1585920,1639680,1670400,1785600,1800960,1908480,1946880
%N Numbers k such that A051378(k) > 2*k and A333926(k) <= 2*k.
%C (1+e)-abundant numbers are numbers k such that A051378(k) > 2*k, i.e., numbers k whose sum of (1+e)-divisors exceeds 2*k.
%C Since all the recursive divisors (see A282446) of a number are also its (1+e)-divisors, the sequence of (1+e)-abundant numbers includes all the recursive abundant numbers (A333928). The first 21387 (1+e)-abundant numbers are also recursive abundant numbers. Therefore, this sequence includes only the (1+e)-abundant numbers that are not recursive abundant numbers.
%H Amiram Eldar, <a href="/A349284/b349284.txt">Table of n, a(n) for n = 1..10000</a>
%e 126720 is a term since A051378(126720) = 261144 > 2*126720 = 253440 and A333926(126720) = 246168 < 253440.
%t oesigma[1] = 1; oesigma[n_] := Times @@ (1 + Sum[First[#]^d, {d, Divisors[Last[#]]}] &) /@ FactorInteger[n]; recDivQ[n_, 1] = True; recDivQ[n_, d_] := recDivQ[n, d] = Divisible[n, d] && AllTrue[FactorInteger[d], recDivQ[IntegerExponent[n, First[#]], Last[#]] &]; recDivs[n_] := Select[Divisors[n], recDivQ[n, #] &]; f[p_, e_] := 1 + Total[p^recDivs[e]]; recsigma[1] = 1; recsigma[n_] := Times @@ (f @@@ FactorInteger[n]); Select[Range[10^6], oesigma[#] > 2*# && recsigma[#] <= 2*# &]
%Y Cf. A049599, A049603, A051378, A282446, A333926, A333928.
%K nonn
%O 1,1
%A _Amiram Eldar_, Nov 13 2021