A348696 Numbers m such that there is at least one smaller number k < m with the same harmonic mean of divisors as m.

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

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

Crossrefs

Cf. A099377, A099378, A348697.

Sequence in context: A358778 A359597 A218417 * A274434 A325569 A372567

Adjacent sequences: A348693 A348694 A348695 * A348697 A348698 A348699

Keyword

nonn

Author

Amiram Eldar, Oct 30 2021

Status

approved