

A348696


Numbers m such that there is at least one smaller number k < m with the same harmonic mean of divisors as m.


2



135, 224, 496, 936, 1485, 1488, 1755, 2295, 2464, 2565, 2912, 3105, 3808, 3915, 4185, 4256, 4464, 4680, 4995, 5152, 5456, 5535, 5805, 6345, 6448, 6496, 6552, 6860, 6944, 7155, 7965, 8235, 8288, 8432, 9045, 9184, 9424, 9585, 9632, 9855, 10296, 10528, 10665, 10976
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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



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


CROSSREFS



KEYWORD

nonn


AUTHOR



STATUS

approved



