A339678 Lesser of amicable pair (a, b) such that the sum of their number of divisors d(a) + d(b) sets a new record.

220, 1184, 6232, 10744, 12285, 67095, 69615, 522405, 1175265, 1798875, 4482765, 5730615, 9773505, 10634085, 34765731, 203972715, 211319745, 558410475, 1131258975, 2221700481, 3900906009, 4416880923, 9357224877, 36853129467, 139043711025, 200453238531, 200795248485

Offset

1,1

Comments

The larger counterparts are in A339679.

The corresponding sums of numbers of divisors are 18, 24, 28, 32, 48, 64, 72, ... (see the link for more values).

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

Links

Amiram Eldar, Table of n, a(n) for n = 1..55

Sergei Chernykh, Amicable pairs list.

Amiram Eldar, Table of n, a(n), A339679(n), A000005(a(n)) + A000005(A339679(n)) for n = 1..55

Example

The least pair of amicable numbers, (220, 284), has a sum of numbers of divisors d(220) + d(284) = 12 + 6 = 18.
The second pair, (1184, 1210) has a larger sum: d(1184) + d(1210) = 12 + 12 = 24.
The next pair with a larger sum is (6232, 6368) whose sum is d(6232) + d(6368) = 16 + 12 = 28.

Mathematica

s[n_] := DivisorSigma[1, n] - n; dm = 0; seq = {}; Do[m = s[n]; If[m > n && s[m] == n && (d = Plus @@ DivisorSigma[0, {n, m}]) > dm, dm = d; AppendTo[seq, n]], {n, 1 , 10^6}]; seq

Crossrefs

Cf. A000005, A002025, A002046, A063990, A328043, A339679.

Sequence in context: A234969 A002025 A260086 * A339682 A241615 A180219

Adjacent sequences: A339675 A339676 A339677 * A339679 A339680 A339681

Keyword

nonn

Author

Amiram Eldar, Dec 12 2020

Status

approved