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Lesser of augmented bi-unitary amicable pair.
2

%I #17 Mar 16 2019 15:27:54

%S 434784,1100176,1252216,1754536,2166136,2362360,3064096,6224890,

%T 7626136,7851256,7950096,9026235,9581320,12494856,13324311,14192080,

%U 15218560,15243424,15422536,19028296,19466560,19555360,29180466,36716680,37542190,40682824,44044000,44588896

%N Lesser of augmented bi-unitary amicable pair.

%C 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).

%C The larger members are in A306868.

%H Amiram Eldar, <a href="/A306867/b306867.txt">Table of n, a(n) for n = 1..509</a> (terms below 2*10^11, from David Moews's site).

%H David Moews, <a href="http://djm.cc/amicable.html">Perfect, amicable and sociable numbers</a>.

%e 434784 is in the sequence since it is the lesser of the amicable pair (434784, 871585): bsigma(434784) = bsigma(871585) = 1306368 = 434784 + 871585 - 1.

%t 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

%Y Cf. A007992, A126174, A188999, A292980, A306868.

%K nonn

%O 1,1

%A _Amiram Eldar_, Mar 14 2019