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 A347077 #23 Apr 19 2024 18:00:44
%S A347077 15063,18519,49841,137607,179943,203345,412763,421307,517334,881851,
%T A347077 1102204,2003233,2831435,3869018,17378593,76645063,107594182,
%U A347077 118012619,190791881,418588841,447287713,475734745,632799289,661709127,664171759,900701138,998754443,1756922665
%N A347077 Numbers m such that sigma(m) / tau(m) = sigma(m - 1) / tau(m - 1) + sigma(m + 1) / tau(m + 1).
%C A347077 Numbers m such that A057020(m) / A057021(m) = A057020(m - 1) / A057021(m - 1) + A057020(m + 1) / A057021(m + 1).
%C A347077 Corresponding values of fractions sigma(m) / tau(m): 5022, 6174, 7128, 45870, 59982, 31008, 111132, 106680, 99636, 220948, 163044, 263160, 449712, 726864, 2278152, ...
%e A347077 sigma(15063) / tau(15063) = sigma(15062) / tau(15062) + sigma(15064) / tau(15064); 20088 / 4 = 23976 / 8 + 32400 / 16; 5022 = 2997 + 2025.
%t A347077 r[n_] := Divide @@ DivisorSigma[{1, 0}, n]; s = {}; r1 = r[1]; r2 = r[2]; Do[r3 = r[n]; If[r2 == r1 + r3, AppendTo[s, n - 1]]; r1 = r2; r2 = r3, {n, 3, 4*10^6}]; s (* _Amiram Eldar_, Aug 16 2021 *)
%t A347077 Flatten[Position[Partition[Table[DivisorSigma[1,n]/DivisorSigma[0,n],{n,900000}],3,1],_?(#[[2]] == #[[1]]+#[[3]]&),1,Heads->False]]+1 (* The program generates the first 10 terms of the sequence. *) (* _Harvey P. Dale_, Apr 19 2024 *)
%o A347077 (Magma) [m: m in [2..10^6] | (&+Divisors(m) / #Divisors(m)) eq (&+Divisors(m - 1) / #Divisors(m - 1)) + (&+Divisors(m + 1) / #Divisors(m + 1))]
%Y A347077 Cf. A000005 (tau), A000203 (sigma), A057020, A057021.
%K A347077 nonn
%O A347077 1,1
%A A347077 _Jaroslav Krizek_, Aug 15 2021
%E A347077 a(16)-a(18) from _Jon E. Schoenfield_, Aug 15 2021
%E A347077 a(19)-a(28) from _Amiram Eldar_, Aug 16 2021