OFFSET
1,1
COMMENTS
The corresponding values of k (the least in case there are more than one) are 84, 120, 140, 864, 924, 420, 1092, 1428, 1320, 1596, ... (see the link for more values).
The least term m with more than one smaller number k with the same harmonic mean of divisors as m is m = a(1237) = A348697(1) = 321048 with k = 201096 and 296352.
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000
Amiram Eldar, Table of n, a(n), least k for n=1..1000
EXAMPLE
135 is a term since the harmonic mean of divisors of 135 is 9/2, and it is also the harmonic mean of divisors of 84 which is smaller than 135.
MATHEMATICA
h = Table[DivisorSigma[0, n]/DivisorSigma[-1, n], {n, 1, 10000}]; i = Position[(t = Tally[h])[[;; , 2]], _?(# > 1 &)] // Flatten; Position[h, #][[2 ;; -1]] & /@ t[[i, 1]] // Flatten // Sort
KEYWORD
nonn
AUTHOR
Amiram Eldar, Oct 30 2021
STATUS
approved