OFFSET
1,1
COMMENTS
Equivalently, numbers that are equal to the sum of their proper bi-unitary divisors, with one of them taken with a minus sign.
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000
EXAMPLE
48 is in the sequence since 48 = 1 + 2 + 3 - 6 + 8 + 16 + 24 is the sum of its proper bi-unitary divisors with one of them, 6, taken with a minus sign.
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]); buDivQ[n_, 1] = True; buDivQ[n_, div_] := If[Mod[#2, #1] == 0, Last@Apply[Intersection, Map[Select[Divisors[#], Function[d, CoprimeQ[d, #/d]]] &, {#1, #2/#1}]] == 1, False] & @@ {div, n}; buAdmQ[n_] := (ab = bsigma[n] - 2 n) > 0 && EvenQ[ab] && ab/2 < n && Divisible[n, ab/2] && buDivQ[n, ab/2]; Select[Range[1000], buAdmQ]
CROSSREFS
KEYWORD
nonn
AUTHOR
Amiram Eldar, May 18 2020
STATUS
approved