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 A283160 #27 Dec 20 2024 02:42:07
%S A283160 0,2,3,8,9,13,14,16,465,467,468,472,473,478,479,481,521,523,524,529,
%T A283160 530,534,535,537,1072,1074,1075,1079,1080,1085,1086,1088,1128,1130,
%U A283160 1131,1136,1137,1141,1142,1144,1744,1746,1747,1751,1752,1757,1758,1760,1800,1802,1803,1808,1809,1813,1814
%N A283160 Numbers k such that there is exactly one solution to the equation sigma(x) = 2^k, where sigma(x) denotes the sum of the divisors of x.
%C A283160 Numbers n such that there is a unique subset S of the Mersenne exponents A000043 summing to n. - _Charles R Greathouse IV_, Mar 07 2017
%H A283160 Charles R Greathouse IV, <a href="/A283160/b283160.txt">Table of n, a(n) for n = 1..168</a>
%F A283160 A063883(a(n)) = 1.
%e A283160 8 is in this sequence that k = 217 is the only number having sigma(k) = 2^8.
%t A283160 With[{e = MersennePrimeExponent[Range[16]]}, Select[Range[0, e[[-1]]], SeriesCoefficient[Series[Product[1 + x^e[[i]], {i, 1, Length[e]}], {x, 0, #}], #] == 1 &]] (* _Amiram Eldar_, Dec 20 2024 *)
%o A283160 (PARI) is(n)=my(N=2^n,s); for(k=1,N, if(sigma(k)==N && s++>1, return(0))); s \\ _Charles R Greathouse IV_, Mar 07 2017
%o A283160 (PARI) list(lim)=my(v=List(),M=[2,3,5,7,13,17,19,31,61,89,107,127,521,607,1279,2203,2281,3217,4253,4423,9689,9941,11213,19937,21701,23209,44497,86243,110503,132049,216091,756839,859433,1257787,1398269,2976221,3021377,6972593,13466917,20996011,24036583,25964951,30402457,32582657,37156667], x='x,P); if(lim>M[#M], error("Need more Mersenne exponents to compute further")); M=select(p->p<=lim,M); P=prod(i=1,#M,1+x^M[i],O(x^(lim\1+1))+1); for(i=0,lim, if(polcoeff(P,i)==1, listput(v,i))); P=0; Vec(v) \\ _Charles R Greathouse IV_, Mar 07 2017
%Y A283160 Cf. A000203, A046528, A063883, A078426, A247956.
%K A283160 nonn
%O A283160 1,2
%A A283160 _Juri-Stepan Gerasimov_, Mar 01 2017
%E A283160 a(9)-a(55) from _Charles R Greathouse IV_, Mar 07 2017