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Numbers k where the ratios A099378(k)/k reach a record value.
0

%I #24 Nov 02 2021 13:20:48

%S 1,2,4,8,16,36,144,576,900,3600,14400,32400,129600,435600,6969600,

%T 8643600,34574400,77792400,311169600,2498000400,2800526400,7779240000,

%U 9992001600,22482003600

%N Numbers k where the ratios A099378(k)/k reach a record value.

%C Are there nonsquare terms in this sequence that are larger than 8?

%e The first 4 ratios A099378(k)/k, for k = 1 to 4, are 1, 3/2, 2/3 and 7/4. The record values occur at k = 1, 2 and 4, the first 3 terms of this sequence.

%t r[n_] := Denominator[DivisorSigma[0, n]/DivisorSigma[-1, n]]/n; s = {}; rm = 0; Do[If[(r1 = r[n]) > rm, rm = r1; AppendTo[s, n]], {n, 1, 5*10^5}]; s

%Y Cf. A099377, A099378, A348414.

%K nonn,more

%O 1,2

%A _Amiram Eldar_, Nov 02 2021