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..96
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
KEYWORD
nonn
AUTHOR
Amiram Eldar, Jun 25 2020
STATUS
approved