%I #4 Dec 12 2020 19:52:34

%S 220,280540,1669910,56512610,133089500,8376676490,24631297425,

%T 688539661425,724641414350,92371445691525,3599848247084570,

%U 7526776592305828,14223210473604152536,35367855263480783043

%N Lesser of amicable pair a < b such that the ratio of their number of divisors d(a)/d(b) sets a new record.

%C The larger counterparts are in A339681.

%C The corresponding ratios are 2, 3, 4, 16/3, 8, 12, 16, 18, 24, 27, 32, 48, 64, 96, ...

%C The terms were calculated using data from Chernykh's site.

%H Sergei Chernykh, <a href="http://sech.me/ap/">Amicable pairs list</a>.

%e The least pair of amicable numbers, (220, 284), has a ratio of the numbers of divisors d(220)/d(284) = 12/6 = 2.

%e The next pair with a larger ratio is (280540, 365084) whose ratio is d(280540)/d(365084) = 36/12 = 3.

%t s[n_] := DivisorSigma[1, n] - n; rm = 0; seq = {}; Do[m = s[n]; If[m > n && s[m] == n && (r = Divide @@ DivisorSigma[0, {n, m}]) > rm, rm = r; AppendTo[seq, n]], {n, 1, 10^7}]; seq

%Y Cf. A000005, A002025, A002046, A063990, A328063, A339681.

%K nonn,more

%O 1,1

%A _Amiram Eldar_, Dec 12 2020