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 A081175 #27 Dec 16 2022 09:03:11
%S A081175 1,3,5,6,9,10,14,15,17,21,28,30,33,36,45,55,65,66,78,91,98,100,105,
%T A081175 120,129,136,140,153,171,190,204,210,225,231,253,257,276,285,300,325,
%U A081175 351,354,378,385,406,435,441,465,496,506,513,528,561,595,630,650,666,703
%N A081175 Numbers of the form Sum_{i=1..k} i^j, j >= 1, k >= 1.
%C A081175 Union of sums of k-th powers, for k >= 1.
%H A081175 Robert Israel, <a href="/A081175/b081175.txt">Table of n, a(n) for n = 1..10000</a>
%H A081175 Michael Penn, <a href="https://www.youtube.com/watch?v=pACLBI6ZQgw">an excruciatingly deep dive into the power sum.</a>, YouTube video, 2022.
%e A081175 30 is in the set because 30 = 1^2 + 2^2 + 3^2 + 4^2 (j=2, k=4).
%p A081175 N:= 1000: # to get all terms <= N
%p A081175 A:=select(`<=`,{1, seq(seq(sum(i^k,i=1..m), m=2..floor((N*(k+1))^(1/(k+1)))),k = 1 ..ilog2(N-1))},N):
%p A081175 sort(convert(A,list)); # _Robert Israel_, Jan 26 2015
%t A081175 Take[ Union[ Flatten[ Table[ Sum[ i^j, {i, 1, n}], {j, 1, 9}, {n, 1, 40}]]], 60]
%Y A081175 Cf. A000217, A000330, A000537, A000538, A000539, A000540, A000541, A000542, A007487, A023002.
%Y A081175 For primes in this sequence see A164307.
%K A081175 nonn,easy
%O A081175 1,2
%A A081175 _N. J. A. Sloane_, Apr 18 2003
%E A081175 Corrected and extended by _Robert G. Wilson v_, May 08 2003