This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A335290 #9 May 31 2020 02:12:28
%S A335290 6,28,350,490,496,770,910,1190,1330,1610,2030,2170,2590,2870,3010,
%T A335290 3290,3710,4130,4270,4690,4970,5110,5530,5810,6230,6790,7070,7210,
%U A335290 7490,7630,7910,8128,8890,9170,9196,9590,9730,15884,19228,24244,25916,30932,34276,35948
%N A335290 Primitive pseudoperfect numbers (A006036) that are not primitive abundant (A071395).
%C A335290 Includes all the perfect numbers (A000396). The nonperfect terms have an abundant proper divisor which is not pseudoperfect, i.e., a proper divisor which is a weird number (A006037).
%C A335290 The first term with one weird divisor is a(3) = 350, having the weird divisor 70.
%C A335290 The first term with 2 weird divisors is a(202) = 658312, having the 2 weird divisors 9272 and 10792.
%C A335290 The first term with 3 weird divisors is a(353) = 1574930, having the 3 weird divisors 70, 10430 and 10570.
%H A335290 Amiram Eldar, <a href="/A335290/b335290.txt">Table of n, a(n) for n = 1..2500</a>
%e A335290 350 is a term since it is pseudoperfect: 1 + 5 + 14 + 35 + 50 + 70 + 175 = 350. All of its proper divisors, {1, 2, 5, 7, 10, 14, 25, 35, 50, 70, 175} are not pseudoperfect, and it is not primitive abundant, since its divisor 70 is abundant.
%t A335290 pspQ[n_] := Module[{d = Most @ Divisors[n], x}, Plus @@d >= n && SeriesCoefficient[Series[Product[1 + x^d[[i]], {i, Length[d]}], {x, 0, n}], n] > 0]; primPspQ[n_] := pspQ[n] && AllTrue[Most @ Divisors[n], !pspQ[#] &]; primAbQ[n_] := DivisorSigma[1, n] > 2*n && AllTrue[Most @ Divisors[n], DivisorSigma[1, #] < 2*# &]; Select[Range[1000], primPspQ[#] && !primAbQ[#] &]
%Y A335290 Cf. A000396, A006036, A006037, A071395, A306987.
%K A335290 nonn
%O A335290 1,1
%A A335290 _Amiram Eldar_, May 30 2020