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 A317412 #18 Jun 11 2023 23:29:19
%S A317412 78,348,666,820,860,1014,1272,1326,1416,1464,1482,1794,1830,2010,2130,
%T A317412 2190,2262,2418,2628,2844,2886,2988,3198,3204,3320,3354,3560,3666,
%U A317412 3738,4074,4134,4602,4656,4758,4848,4944,5136,5226,5232,5424,5538,5694,5886,6102,6162,6328
%N A317412 Practical numbers (A005153) that are not numbers whose divisors increase by a factor of 2 or less (A174973).
%C A317412 Numbers that appear in A005153 but not in A174973.
%H A317412 Wikipedia, <a href="https://www.wikipedia.org/wiki/Practical_number">Practical number</a>.
%H A317412 Wikipedia, <a href="https://www.wikipedia.org/wiki/Complete_sequence">"Complete" sequence</a>. [Wikipedia calls a sequence "complete" (sic) if every positive integer is a sum of distinct terms. This name is extremely misleading and should be avoided. - _N. J. A. Sloane_, May 20 2023]
%e A317412 a(1)=78 because it is practical. It has divisors 1, 2, 3, 6, 13, 26, 39, 78, and 13/6 > 2. This is the first occurrence.
%t A317412 PracticalQ[n_] := Module[{f, p, e, prod=1, ok=True}, If[n<1||(n>1&&OddQ[n]), False, If[n==1, True, f=FactorInteger[n]; {p, e}=Transpose[f]; Do[If[p[[i]]>1+DivisorSigma[1, prod], ok=False; Break[]]; prod = prod*p[[i]]^e[[i]], {i, Length[p]}]; ok]]]; Dens2DivQ[n_] := Module[{lst=Divisors[n]}, Do[ok=False; If[lst[[m+1]]/lst[[m]]>2, Break[]]; ok=True, {m, 1, Length[lst]-1}]; ok]; Select[Range[10000], PracticalQ[#]&&!Dens2DivQ[#] &]
%Y A317412 Cf. A005153, A174973.
%K A317412 nonn
%O A317412 1,1
%A A317412 _Frank M Jackson_, Jul 27 2018