OFFSET
1,1
COMMENTS
This list excludes 1 and prime numbers, which by definition have no proper divisors.
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[Range[2000], Function[ n, ! PrimeQ[n] &&
IntegerQ[Plus @@ Map[#/EulerPhi[#] &, DeleteCases[Divisors[n], 1 | n]]]]]
q[n_] := CompositeQ[n] && IntegerQ[DivisorSum[n, #/EulerPhi[#] &, 1 < # < n &]]; Select[Range[4000], q] (* Amiram Eldar, Jul 01 2022 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Olivier Gérard, Mar 29 2014
STATUS
approved