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 A174533 #18 Sep 26 2019 09:07:23
%S A174533 70,350,490,770,910,945,1190,1330,1575,1610,1750,2030,2170,2205,2450,
%T A174533 2584,2590,2835,2870,3010,3128,3290,3430,3465,3710,3850,3944,4095,
%U A174533 4130,4216,4270,4550,4690,4725,5355,5390,5775,5950,5985,6370,6615,6650,6825
%N A174533 Almost practical numbers.
%C A174533 For such numbers n, all but 2 of the numbers from 1 to sigma(n) can be represented as the sum of distinct divisors of n. Because the sum of distinct divisors of practical numbers, A005153, can represent all numbers from 1 to sigma(n), it seems fitting to call the numbers in this sequence "almost practical". Stewart characterized the odd numbers in this sequence, for which the two excluded numbers are always 2 and sigma(n)-2. However, another possibility is for 4 and sigma(n)-4 to be excluded, which occurs for even numbers in this sequence. See A174534 and A174535.
%C A174533 Numbers k such that both k and k+1 are in this sequence: 134504, 636615, 648584, ... - _Amiram Eldar_, Sep 25 2019
%C A174533 Only numbers <= ceiling(sigma(n) / 2) must be checked if they're a sum as if m isn't a sum of distinct divisors then sigma(n) - m isn't either. - _David A. Corneth_, Sep 25 2019
%H A174533 Amiram Eldar, <a href="/A174533/b174533.txt">Table of n, a(n) for n = 1..3000</a>
%H A174533 B. M. Stewart, <a href="http://doi.org/10.2307/2372651">Sums of distinct divisors</a>, American Journal of Mathematics, Vol. 76, No. 4 (1954), pp. 779-785.
%e A174533 The divisors of 70 are 1, 2, 5, 7, 10, 14, 35, 70 and sigma(70) = 144. The numbers from 1 to 144 that can be represented as the sum of distinct divisors of 70 are 1, 2, 3=2+1, 5, 6=5+1, 7, ... , 138=70+35+14+10+7+2, 139=70+35+14+10+7+2+1, 141=70+59+7+5, 142=70+59+7+5+1, 143=70+59+7+5+2, 144=70+59+7+5+2+1. The only two excluded numbers are 4 and 140=sigma(70)-4 as mentionned in comments. - _Bernard Schott_, Sep 25 2019
%t A174533 CountNumbers[n_] := Module[{d=Divisors[n],t,x}, t=CoefficientList[Product[1+x^i, {i,d}], x]; Count[Rest[t], _?(#>0&)]]; Select[Range[1000], CountNumbers[ # ] == DivisorSigma[1,# ]-2&]
%Y A174533 Cf. A005153, A174534, A174535.
%K A174533 nonn
%O A174533 1,1
%A A174533 _T. D. Noe_, Mar 21 2010