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

1,1

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.

Links

Table of n, a(n) for n=1..14.

Sergei Chernykh, Amicable pairs list.

Example

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.

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

Crossrefs

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

Sequence in context: A282591 A091756 A167825 * A266237 A371899 A159565

Adjacent sequences: A339677 A339678 A339679 * A339681 A339682 A339683

Keyword

nonn,more

Author

Amiram Eldar, Dec 12 2020

Status

approved