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Numbers with record values of the denominator of the harmonic mean of their divisors.
3

%I #10 Oct 20 2021 07:16:29

%S 1,2,4,8,16,36,64,100,128,144,256,324,400,512,576,900,1296,1600,1936,

%T 2304,3600,5184,6400,8100,9216,10404,11664,14400,17424,20736,22500,

%U 30276,32400,41616,46656,57600,76176,90000,108900,129600,166464,202500,230400,260100

%N Numbers with record values of the denominator of the harmonic mean of their divisors.

%C The corresponding record values are 1, 3, 7, 15, 31, 91, 127, 217, 255, 403, ... (see the link for more values).

%H Amiram Eldar, <a href="/A348414/b348414.txt">Table of n, a(n) for n = 1..200</a>

%H Amiram Eldar, <a href="/A348414/a348414.txt">Table of n, a(n), A099378(a(n)) for n = 1..200</a>

%e The first 4 terms of A099378 are 1, 3, 2 and 7. The record values, 1, 3 and 7, occur at 1, 2 and 4, the first 3 terms of this sequence.

%t d[n_] := Denominator[DivisorSigma[0, n]/DivisorSigma[-1, n]]; dm = 0; s = {}; Do[dn = d[n]; If[dn > dm, dm = dn; AppendTo[s, n]], {n, 1, 10^6}]; s

%Y Cf. A099377, A099378.

%K nonn

%O 1,2

%A _Amiram Eldar_, Oct 17 2021