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A239887
Integer values of the proper divisor balance of composite numbers.
4
2, 4, 6, 8, 3, 8, 16, 7, 10, 24, 14, 9, 12, 32, 17, 21, 6, 14, 40, 39, 31, 9, 20, 28, 16, 48, 45, 34, 35, 18, 18, 33, 41, 56, 74, 59, 53, 19, 26, 42, 74, 50, 20, 9, 64, 73, 49, 46, 39, 32, 5, 40, 49, 32, 22, 72, 25, 109, 87, 130, 68, 21, 97, 66, 56, 137, 8, 67
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
Cf. A023898, A023899 for the versions with all divisors included.
Sequence in context: A220102 A308080 A179657 * A354721 A355506 A241012
KEYWORD
nonn
AUTHOR
Olivier Gérard, Mar 29 2014
STATUS
approved