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%I #11 Oct 12 2022 04:31:59
%S 20,88,104,272,304,368,464,550,572,650,748,945,1184,1312,1376,1430,
%T 1504,1575,1696,1870,1888,1952,2002,2090,2205,2210,2470,2530,2584,
%U 2990,3128,3190,3230,3410,3465,3496,3770,3944,4070,4095,4216,4288,4408,4510,4544,4672
%N Primitive abundant numbers (A071395) that are pseudoperfect (A005835).
%C By definition these numbers are also primitive pseudoperfect (A006036).
%C Benkoski and Erdős proved that this sequence is infinite, since it includes all the numbers of the form 2^k * p with p a prime such that 2^k < p < 2^(k+1).
%H Amiram Eldar, <a href="/A306987/b306987.txt">Table of n, a(n) for n = 1..10000</a>
%H S. J. Benkoski and P. Erdős, <a href="http://dx.doi.org/10.1090/S0025-5718-1974-0347726-9">On weird and pseudoperfect numbers</a>, Math. Comp. 28 (1974), 617-623. Corrigendum: Math. Comp. 29 (1975), 673-674.
%t paQ[n_]:=DivisorSigma[1, n] > 2n && Times @@ Boole@ Map[DivisorSigma[1, #] < 2 # &, Most@ Divisors@ n] == 1; psQ[n_]:=Module[{d= Most[Divisors[n] ]}, SeriesCoefficient[Series[Product[1 + x^d[[i]], {i, Length[d]}], {x, 0, n}], n] > 0]; Select[Range[5000], paQ[#]&&psQ[#]&] (* after _Michael De Vlieger_ at A071395 and _T. D. Noe_ at A005835 *)
%Y Cf. A005835, A006036, A071395.
%K nonn
%O 1,1
%A _Amiram Eldar_, Mar 18 2019
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