A339680 Lesser of amicable pair a < b such that the ratio of their number of divisors d(a)/d(b) sets a new record.

220, 280540, 1669910, 56512610, 133089500, 8376676490, 24631297425, 688539661425, 724641414350, 92371445691525, 3599848247084570, 7526776592305828, 14223210473604152536, 35367855263480783043

Offset: 1

Author

Amiram Eldar, Dec 12 2020

Keywords

• nonn
• more

Comments

The larger counterparts are in A339681.

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

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

Examples

			The least pair of amicable numbers, (220, 284), has a ratio of the numbers of divisors d(220)/d(284) = 12/6 = 2.
The next pair with a larger ratio is (280540, 365084) whose ratio is d(280540)/d(365084) = 36/12 = 3.
		

Links

• Sergei Chernykh, Amicable pairs list.

Crossrefs

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

Programs

Mathematica

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