OFFSET
1,1
COMMENTS
1 and all primes have proper divisor balance 0. These values are not included in this list.
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..1000 (terms 1..267 from Vincenzo Librandi)
FORMULA
Proper divisor balance of n = Sum_{1 < d < n and divides n} {d / phi(d)} where phi is Euler's phi function.
MATHEMATICA
Select[Array[Function[n, Plus @@ Map[#/EulerPhi[#] &, DeleteCases[Divisors[n], 1 | n]]], 3000], Positive[#] && IntegerQ[#] &]
Select[Table[Total[#/EulerPhi[#]&/@Most[Rest[Divisors[n]]]], {n, 2, 3000}], Positive[ #]&&IntegerQ[#]&] (* Harvey P. Dale, Oct 31 2020 *)
s[n_] := DivisorSum[n, #/EulerPhi[#] &, 1 < # < n &]; Select[s /@ Select[Range[10^4], CompositeQ], IntegerQ] (* Amiram Eldar, Jul 01 2022 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Olivier Gérard, Mar 29 2014
STATUS
approved