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 A175849 #12 Feb 23 2020 07:09:17 %S A175849 1,8,9,215,458,520,2232,3251,3634,5349,9489,10051,10463,14072,14705, %T A175849 17463,27812,46552,55889,79614,100055,106941,110682,113839,119098, %U A175849 181690,197223,214600,270570,287585,333291,384463,439206,443115,608563,767496,1097448,1335300 %N A175849 Numbers k with property that sum of divisors of k-th triangular number is some m-th triangular number. %H A175849 Amiram Eldar, <a href="/A175849/b175849.txt">Table of n, a(n) for n = 1..226</a> %H A175849 Zak Seidov, <a href="http://zak08.livejournal.com/24800.html">A175849,A175850</a> %F A175849 sigma(T(k)) = T(m); A000203(A000217(k)) = A000217(m). %e A175849 Some pairs of k,m: 1,1; 8,13; 9,12; 215,384; 458,575; 520,783; 2232,4095; 3251,4607; 3634,4095; 5349,6912; 9489,12543; 10051,13824. %t A175849 Select[Range[10^4], IntegerQ @ Sqrt[8*DivisorSigma[1, #*(#+1)/2] + 1] &] (* _Amiram Eldar_, Feb 23 2020 *) %o A175849 (PARI) {for(n=1, 10^7, m=sigma(n*(n+1)/2); issquare(d=1+8*m) && print1(n, ", "))} \\ edited by %Y A175849 Cf. A000203 (sigma(n) = sum of divisors of n), A000217 (triangular numbers), A175850 (corresponding values of m). %K A175849 nonn %O A175849 1,2 %A A175849 _Zak Seidov_, Sep 27 2010 %E A175849 More terms from _Amiram Eldar_, Feb 23 2020