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 A335030 #5 May 20 2020 07:40:25
%S A335030 3,9,10,44,70,102,350,372,1608,3492,6096,10380,44040,100260,180240,
%T A335030 425160,1744560,2425080,5509980,10048080,23614920,97639920,396315360,
%U A335030 900229680,2519017200,3113704440,12870562320,52307529120
%N A335030 Numbers m that are not practical and have an abundancy index sigma(m)/m which is larger than that of any smaller number that is not practical.
%C A335030 None of the terms are superabundant (A004394) since all the superabundant numbers are practical numbers (A005153).
%C A335030 The least term m that is k-abundant (having sigma(m)/m > k) for k = 2, 3, ... is A005101(14) = 70, A068403(896) = 44040, A068404(792087) = 3113704440, ...
%C A335030 What is the least 5-abundant number (A215264) that is not practical?
%e A335030 The first 5 numbers that are not practical are m = 3, 5, 7, 9, 10. Their abundancy indices sigma(m)/m are 1.333..., 1.2, 1.142..., 1.444..., 1.8. The record values occur at 3, 9 and 10.
%t A335030 f[p_, e_] := (p^(e + 1) - 1)/(p - 1); pracQ[fct_] := (ind = Position[fct[[;; , 1]]/(1 + FoldList[Times, 1, f @@@ Most@fct]), _?(# > 1 &)]) == {}; seq = {}; rm = 1; Do[fct = FactorInteger[n]; r = Times@@((First/@fct^ (1+Last/@ fct)-1)/(First/@fct-1))/n; If[r > rm && !pracQ[fct], rm = r; AppendTo[seq, n]], {n, 3, 10^5}]; seq
%Y A335030 Cf. A000203 (sigma), A004394, A005153, A237287, A330244, A335029.
%K A335030 nonn,more
%O A335030 1,1
%A A335030 _Amiram Eldar_, May 20 2020