A306871 Larger of reduced bi-unitary amicable pair.

2295, 20735, 75495, 1148735, 817479, 774375, 1902215, 1341495, 1348935, 2226014, 2421704, 3123735, 3010215, 5644415, 3894344, 4282215, 4994055, 7509159, 12251679, 10106504, 12900734, 20444319, 24519159, 28206815, 31356314, 33362175, 41950359, 36129375, 43321095

Offset

1,1

Comments

A pair m < n are 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 terms are ordered according to their lesser counterparts (A306870).

Links

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

David Moews, Perfect, amicable and sociable numbers.

Example

2295 is in the sequence since it is the larger 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, m]], {n, 1, 10^7}]; s

Crossrefs

Cf. A003503, A126173, A188999, A292981, A306870.

Sequence in context: A163513 A349085 A274359 * A123911 A126173 A083572

Adjacent sequences: A306868 A306869 A306870 * A306872 A306873 A306874

Keyword

nonn

Author

Amiram Eldar, Mar 14 2019

Status

approved