A335291 Numbers m such that the delta(m) = abs(h(m+1) - h(m)) is smaller than delta(k) for all k < m, where h(m) is the harmonic mean of the divisors of m.

1, 2, 4, 91, 272, 20118, 20712, 33998, 42818, 61695, 25274946, 27194929, 34883654, 40406622, 43176318, 47350866, 52680050, 149736013, 154957034, 162929406, 171560153, 187012577, 208015843, 267361097, 300087726, 325189758, 355153181, 443360633, 584803578, 605883413

Offset

1,2

Comments

Apparently, most of the terms m have h(m+1) > h(m) and numerator(delta(m)) = 1.

Can two consecutive numbers have the same harmonic mean of divisors? If yes, then this sequence is finite.

Links

Amiram Eldar, Table of n, a(n) for n = 1..86

Example

The values of delta(k) for the first terms are 0.333..., 0.166..., 0.047..., 0.0357..., ...

Mathematica

h[n_] := n * DivisorSigma[0, n]/DivisorSigma[1, n]; dm = 1; h1 = h[1]; s = {}; Do[h2 = h[n]; d = Abs[h2 - h1]; If[d < dm, dm = d; AppendTo[s, n-1]]; h1 = h2, {n, 2, 10^5}]; s

Crossrefs

Cf. A000005, A000203, A099377, A099378.

Cf. A238380, A335071.

Sequence in context: A270484 A327427 A335571 * A156496 A007534 A299784

Adjacent sequences: A335288 A335289 A335290 * A335292 A335293 A335294

Keyword

nonn

Author

Amiram Eldar, May 30 2020

Status

approved