A306868 Larger of augmented bi-unitary amicable pair.

871585, 1388145, 1483785, 2479065, 2580105, 4895241, 3830625, 7336455, 9100905, 10350345, 16933105, 9843526, 16367481, 24829945, 15706090, 18653745, 27866241, 21080865, 15439545, 23872185, 24401601, 32263905, 53763535, 63075321, 41337555, 60923577, 90245793

Offset

1,1

Comments

A pair m < n is an augmented 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 (A306867).

Links

Amiram Eldar, Table of n, a(n) for n = 1..509 (terms with lesser member below 2*10^11, from David Moews's site).

David Moews, Perfect, amicable and sociable numbers.

Example

871585 is in the sequence since it is the larger of the amicable pair (434784, 871585): bsigma(434784) = bsigma(871585) = 1306368 = 434784 + 871585 - 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. A015630, A126175, A188999, A292981, A306867.

Sequence in context: A182450 A362793 A293373 * A223886 A204509 A271263

Adjacent sequences: A306865 A306866 A306867 * A306869 A306870 A306871

Keyword

nonn

Author

Amiram Eldar, Mar 14 2019

Status

approved