login
A306870
Lesser of reduced bi-unitary amicable pair.
2
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).
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
KEYWORD
nonn
AUTHOR
Amiram Eldar, Mar 14 2019
STATUS
approved