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 A335832 Numbers k with record values of the ratio d(k)/id(k) between the number of divisors and the number of infinitary divisors. 3
 1, 4, 16, 144, 256, 1296, 2304, 20736, 518400, 1679616, 5308416, 12960000, 41990400, 132710400, 429981696, 635040000, 1049760000, 3317760000, 10749542400, 31116960000, 51438240000, 162570240000, 268738560000, 2520473760000, 7965941760000, 13168189440000, 167961600000000 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS This sequence is infinite since the ratio d(k)/id(k) is unbounded. For example, for k = 2^(2^m) we have d(k)/id(k) = (2^m+1)/2. The corresponding record values are 1, 1.5, 2.5, 3.75, 4.5, 6.25, 6.75, 11.25, 16.875, 20.25, ... LINKS Amiram Eldar, Table of n, a(n) for n = 1..87 FORMULA The ratios d(k)/id(k) for k = 1, 2, 3 and 4 are 1, 1, 1 and 3/2. The record values occur at 1 and 4. MATHEMATICA id[1] = 1; id[n_] := Times @@ Flatten[2^DigitCount[#, 2, 1] & /@ FactorInteger[n][[All, 2]]]; f[1] = 1; f[n_] := DivisorSigma[0, n]/id[n]; seq = {}; fm = 0; Do[f1 = f[n]; If[f1 > fm, fm = f1; AppendTo[seq, n]], {n, 1, 10^6}]; seq CROSSREFS Subsequence of A025487. Cf. A000005, A037445, A307870. Sequence in context: A362143 A358289 A156482 * A173346 A319166 A335400 Adjacent sequences: A335829 A335830 A335831 * A335833 A335834 A335835 KEYWORD nonn AUTHOR Amiram Eldar, Jun 25 2020 STATUS approved

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Last modified October 4 19:37 EDT 2023. Contains 365888 sequences. (Running on oeis4.)