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A239886
Composite numbers whose proper divisor balance is an integer.
4
4, 8, 16, 18, 27, 32, 36, 50, 64, 72, 100, 105, 128, 144, 162, 200, 243, 256, 288, 300, 324, 375, 392, 400, 512, 576, 648, 700, 800, 850, 1024, 1100, 1134, 1152, 1200, 1296, 1350, 1352, 1458, 1600, 1620, 1650, 2048, 2187, 2304, 2592, 2850, 2916, 3078, 3100, 3125
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
Cf. A239887 (corresponding values of the proper divisor balance).
Cf. A000010, A023898, A023899 for the versions with all divisors included.
Sequence in context: A312778 A312779 A312780 * A312781 A312782 A312783
KEYWORD
nonn
AUTHOR
Olivier Gérard, Mar 29 2014
STATUS
approved