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

Author

Amiram Eldar, Mar 14 2019

Keywords

• nonn

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.

Examples

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

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.

Crossrefs

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

Programs

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