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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
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified June 18 13:35 EDT 2021. Contains 345112 sequences. (Running on oeis4.)