A306870 Lesser of reduced bi-unitary amicable pair.

2024, 9504, 62744, 496320, 573560, 677144, 1000824, 1173704, 1208504, 1921185, 2140215, 2198504, 2312024, 2580864, 3847095, 4012184, 4682744, 5416280, 6618080, 9247095, 12500865, 12970880, 13496840, 14371104, 23939685, 25942784, 26409320, 28644704, 34093304

Offset

1,1

Comments

A pair m < n is a reduced bi-unitary amicable pair if bsigma(m) = bsigma(n) = m + n + 1, where bsigma(n) is the sum of bi-unitary divisors of n (A188999).

The larger members are in A306871.

Links

Amiram Eldar, Table of n, a(n) for n = 1..528 (terms below 2*10^11, from David Moews's site).

David Moews, Perfect, amicable and sociable numbers.

Example

2024 is in the sequence since it is the lesser of the amicable pair (2024, 2295): bsigma(2024) = bsigma(2295) = 4320 = 2024 + 2295 + 1.

Mathematica

fun[p_, e_]:=If[OddQ[e], (p^(e+1)-1)/(p-1), (p^(e+1)-1)/(p-1)-p^(e/2)]; bsigma[1] = 1; bsigma[n_] := Times @@ (fun @@@ FactorInteger[n]); f[n_] := bsigma[n] - n - 1; s={}; Do[m = f[n]; If[m > n && f[m] == n, AppendTo[s, n]], {n, 1, 10^7}]; s

Crossrefs

Cf. A003502, A126172, A188999, A292980, A306871.

Sequence in context: A126821 A333057 A156855 * A126172 A183999 A360216

Adjacent sequences: A306867 A306868 A306869 * A306871 A306872 A306873

Keyword

nonn

Author

Amiram Eldar, Mar 14 2019

Status

approved