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 A261811 #25 Jul 26 2022 22:03:10
%S A261811 4,8,12,13,16,20,24,32,36,40,44,48,52,56,64,68,72,76,77,80,84,88,96,
%T A261811 100,104,108,112,116,120,122,128,132,136,140,141,144,148,152,160,164,
%U A261811 168,172,176,180,184,192,196,200,204,205,208,212,216,224,228,232,236,240,244,248,256,260
%N A261811 Numbers m such that Sum_{k>=0} k^m/3^k is an integer.
%C A261811 For a denominator with an exponent base of 2, this series is A000027; for bases more than 3, no integer values are known. All powers of 2 greater than 2 are believed to be in this sequence. - _Drake Thomas_, May 13 2016
%H A261811 RavenclawPrefect, <a href="http://math.stackexchange.com/questions/1417433/when-is-sum-n-0-infty-fracnk3n-an-integer">When is Sum_{k>=0} k^n/3^k an integer?</a>
%e A261811 4 is in the list because 0^4/3^0 + 1^4/3^1 + 2^4/3^2 + ... = 15 is an integer.
%t A261811 Select[Range@ 260, IntegerQ[Sum[k^#/3^k, {k, 0, Infinity}]] &] (* _Michael De Vlieger_, Sep 02 2015 *)
%t A261811 Select[Range @ 260, IntegerQ@ HurwitzLerchPhi[1/3, -#, 0] &] (* _Giovanni Resta_, Sep 10 2015, fixed by _Vaclav Kotesovec_, Mar 23 2018 *)
%K A261811 nonn
%O A261811 1,1
%A A261811 _Hagen von Eitzen_, Sep 01 2015