OFFSET
1,2
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..1000 from Vincenzo Librandi)
FORMULA
Divisor balance of n = Sum_{d divides n} {d / phi(d)} where phi is Euler's phi function.
EXAMPLE
45 is in this list because its divisors are 1,3,5,9,15 and 45, the corresponding fractions are : (1, 3/2, 5/4, 3/2, 15/8, 15/8) and their sum is 9, which is an integer.
MATHEMATICA
Select[ Range[ 2000 ], Function[ n, IntegerQ[ Plus @@ Map[ #/EulerPhi[ # ]&, Divisors[ n ] ] ] ] ]
dbiQ[n_]:=Module[{d=Divisors[n]}, IntegerQ[Total[d/EulerPhi[d]]]]; Select[ Range[ 2000], dbiQ] (* Harvey P. Dale, Jul 25 2016 *)
q[n_] := IntegerQ[DivisorSum[n, #/EulerPhi[#] &]]; Select[Range[1800], q] (* Amiram Eldar, Jul 01 2022 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
STATUS
approved