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 A347077 Numbers m such that sigma(m) / tau(m) = sigma(m - 1) / tau(m - 1) + sigma(m + 1) / tau(m + 1). 0
 15063, 18519, 49841, 137607, 179943, 203345, 412763, 421307, 517334, 881851, 1102204, 2003233, 2831435, 3869018, 17378593, 76645063, 107594182, 118012619, 190791881, 418588841, 447287713, 475734745, 632799289, 661709127, 664171759, 900701138, 998754443, 1756922665 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Numbers m such that A057020(m) / A057021(m) = A057020(m - 1) / A057021(m - 1) + A057020(m + 1) / A057021(m + 1). Corresponding values of fractions sigma(m) / tau(m): 5022, 6174, 7128, 45870, 59982, 31008, 111132, 106680, 99636, 220948, 163044, 263160, 449712, 726864, 2278152, ... LINKS Table of n, a(n) for n=1..28. EXAMPLE sigma(15063) / tau(15063) = sigma(15062) / tau(15062) + sigma(15064) / tau(15064); 20088 / 4 = 23976 / 8 + 32400 / 16; 5022 = 2997 + 2025. MATHEMATICA 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 *) 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 *) PROG (Magma) [m: m in [2..10^6] | (&+Divisors(m) / #Divisors(m)) eq (&+Divisors(m - 1) / #Divisors(m - 1)) + (&+Divisors(m + 1) / #Divisors(m + 1))] CROSSREFS Cf. A000005 (tau), A000203 (sigma), A057020, A057021. Sequence in context: A254356 A187423 A186215 * A257017 A257014 A237335 Adjacent sequences: A347074 A347075 A347076 * A347078 A347079 A347080 KEYWORD nonn AUTHOR Jaroslav Krizek, Aug 15 2021 EXTENSIONS a(16)-a(18) from Jon E. Schoenfield, Aug 15 2021 a(19)-a(28) from Amiram Eldar, Aug 16 2021 STATUS approved

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Last modified September 10 17:26 EDT 2024. Contains 375792 sequences. (Running on oeis4.)