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 A317478 #14 Aug 26 2024 18:51:01
%S A317478 6,28,55,496,666,780,1540,2145,6441,6903,8128,15051,21736,36585,44551,
%T A317478 232903,234955,644680,2258875,3186550,3462396,6211050,22174470,
%U A317478 33550336,48437403,62591266,107538445,134898525,153554050,624157446,1309312378,1339937028
%N A317478 Triangular numbers whose sum of divisors is an oblong number.
%C A317478 Includes all the even perfect numbers.
%C A317478 The indices of these triangular numbers are 3, 7, 10, 31, 36, 39, 55, 65, 113, 117, 127, 173, 208, 270, 298, 682, 685, 1135, 2125, 2524, 2631, 3524, 6659, 8191, 9842, 11188, 14665, 16425, 17524, 35331, 51172, 51767, 52019, 52486, 58993, 65585, 97532.
%C A317478 The indices of the corresponding oblong numbers are 3, 7, 8, 31, 38, 48, 63, 63, 95, 104, 127, 144, 224, 255, 224, 512, 575, 1215, 1728, 2448, 3072, 3968, 7695, 8191, 9215, 9792, 12159, 15872, 17576, 37296, 46656, 58239, 63855, 40959, 46080, 62720, 102960.
%C A317478 Number of terms < 10^k, k=1,2,3...: 1, 3, 6, 11, 15, 18, 22, 26, 30, 40, 52, 64, 80, 90, 110, 128, ..., . - _Robert G. Wilson v_, Jul 31 2018
%H A317478 Robert G. Wilson v, <a href="/A317478/b317478.txt">Table of n, a(n) for n = 1..129</a>
%e A317478 55 is in the sequence since sigma(55) = 72 = 8 * 9 is an oblong number.
%t A317478 tri[n_] := n(n+1)/2; aQ[n_] := IntegerQ[Sqrt[4 * DivisorSigma[1, tri[n]] + 1]]; tri[Select[Range[52000], aQ]]
%t A317478 Module[{nn=60000,obno},obno=Table[n(n+1),{n,nn}];Select[Accumulate[Range[nn]],MemberQ[ obno,DivisorSigma[1,#]]&]] (* _Harvey P. Dale_, Aug 26 2024 *)
%Y A317478 Cf. A000203, A000217, A000396, A002378, A083674, A083675, A175849.
%Y A317478 Intersection of A000217 and A236387. - _Michel Marcus_, Jul 30 2018
%K A317478 nonn,easy
%O A317478 1,1
%A A317478 _Amiram Eldar_, Jul 29 2018