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 A291485 #24 Mar 27 2024 09:00:05
%S A291485 1,2,3,5,7,8,12,13,15,18,20,24,27,30,31,32,35,38,39,47,48,51,55,56,62,
%T A291485 63,64,79,80,84,90,92,95,96,104,111,116,119,120,128,135,140,142,143,
%U A291485 144,147,152,155,156,159,160,167,168,170,171,175,176,182,184,188,191,192,195,203,207,208
%N A291485 Numbers m such that sigma(x) = m*(m+1)/2 has at least one solution.
%C A291485 Let b(n) be the smallest k such that sigma(k) is the n-th triangular number, or 0 if no such k exists. For n >= 1, b(n) sequence is 1, 2, 5, 0, 8, 0, 12, 22, 0, 0, 0, 45, 36, 0, 54, 0, 0, 98, 0, 104, 0, 0, 0, 152, 0, 0, 160, 0, 0, 200, ...
%H A291485 Amiram Eldar, <a href="/A291485/b291485.txt">Table of n, a(n) for n = 1..10000</a>
%e A291485 15 is a term because sigma(54) = sigma(56) = sigma(87) = sigma(95) = A000217(15).
%p A291485 N:= 1000: # to get all terms <= N
%p A291485 Sigmas:= {seq(numtheory:-sigma(x),x=1..N*(N+1)/2)}:
%p A291485 select(t -> member(t*(t+1)/2, Sigmas), [$1..N]); # _Robert Israel_, Aug 25 2017
%t A291485 invT[n_] := (Sqrt[8*n+1]-1)/2; Union@ Select[invT /@ DivisorSigma[1, Range[ 208*209/2]], IntegerQ[#] && # <= 208 &] (* _Giovanni Resta_, Aug 25 2017 *)
%Y A291485 Cf. A000203, A000217, A045746.
%K A291485 nonn,easy
%O A291485 1,2
%A A291485 _Altug Alkan_, Aug 24 2017