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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
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
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
KEYWORD
nonn
AUTHOR
Amiram Eldar, May 30 2020
STATUS
approved