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 A078426 #31 May 20 2021 04:48:12
%S A078426 1,4,6,11,470,475,477,480,482,483,484,485,486,487,488,489,490,491,492,
%T A078426 493,494,495,496,497,498,499,500,501,502,503,504,505,506,507,508,509,
%U A078426 510,511,512,513,514,515,516,517,518,519,520,522,525,527,532,1077,1082
%N A078426 Numbers k such that there is no solution to the equation sigma(x) = 2^k, where sigma(x) denotes the sum of the divisors of x.
%C A078426 Numbers that are not a sum of distinct Mersenne exponents (A000043). - _Vladeta Jovovic_, Jan 01 2003
%C A078426 Because there is a large gap between the 31st and 32nd Mersenne exponents, all k between 704338 and 756839 are in this sequence. - _T. D. Noe_, Oct 12 2006
%C A078426 A000203(A180162(a(n))) = 6^a(n), for n > 1. - _Walter Kehowski_, Aug 16 2010
%C A078426 Using all known Mersenne exponents, there are exactly 52935 terms in this sequence. When a new Mersenne prime (with exponent q) is found, there will be no new terms if the sum of the previous Mersenne exponents (A109472) is greater than q - 22.
%D A078426 S. Kravitz, "Beware of the Fifth", Solution to Problem 2309, Journal of Recreational Mathematics, 29(1):76 Baywood NY 1998.
%H A078426 T. D. Noe, <a href="/A078426/b078426.txt">Table of n, a(n) for n = 1..300</a>
%e A078426 a(2)=4 because no positive integer value of x can satisfy sigma(x) = 2^4 = 16.
%t A078426 e={2,3,5,7,13,17,19,31,61,89,107,127,521,607,1279,2203,2281,3217,4253, 4423,9689,9941,11213,19937,21701,23209,44497,86243,110503,132049,216091, 756839,859433,1257787,1398269}; u={0}; Do[u=Union[u, u+e[[k]]], {k,Length[e]}]; Complement[Range[e[[-1]]], u]
%Y A078426 Cf. A000203, A007369, A046528, A063883, A180221 (complement).
%K A078426 nonn
%O A078426 1,2
%A A078426 _Shyam Sunder Gupta_, Dec 29 2002
%E A078426 More terms from _Vladeta Jovovic_, Jan 01 2003
%E A078426 Edited by _N. J. A. Sloane_, Aug 23 2010
%E A078426 Edited by _Max Alekseyev_, Jan 24 2014