A339682 Lesser of amicable pair a < b such that the ratio of their number of divisors d(b)/d(a) sets a new record.

220, 1184, 469028, 11693290, 37784810, 6057622044705, 14772536572365, 35019687151575, 19245649704560895, 42564348058073842, 1004007953218033575, 6778057036176125612

Offset: 1

Author

Amiram Eldar, Dec 12 2020

Keywords

• nonn
• more

Comments

The larger counterparts are in A339683.

The corresponding ratios are 1/2, 1, 2, 3, 4, 16/3, 6, 8, 9, 12, 16, 24, ...

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(284)/d(220) = 6/12 = 1/2.
The next pair with a larger ratio is (1184, 1210) whose ratio is d(1210)/d(1184) = 12/12 = 1.
		

Links

• Sergei Chernykh, Amicable pairs list.

Crossrefs

Cf. A000005, A002025, A002046, A063990, A328255, A339683.

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, {m, n}]) > rm, rm = r; AppendTo[seq, n]], {n, 1, 10^7}]; seq