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%I #18 Jul 01 2022 05:25:55
%S 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,
%T 45,34,35,18,18,33,41,56,74,59,53,19,26,42,74,50,20,9,64,73,49,46,39,
%U 32,5,40,49,32,22,72,25,109,87,130,68,21,97,66,56,137,8,67
%N Integer values of the proper divisor balance of composite numbers.
%C 1 and all primes have proper divisor balance 0. These values are not included in this list.
%H Amiram Eldar, <a href="/A239887/b239887.txt">Table of n, a(n) for n = 1..1000</a> (terms 1..267 from Vincenzo Librandi)
%F Proper divisor balance of n = Sum_{1 < d < n and divides n} {d / phi(d)} where phi is Euler's phi function.
%t Select[Array[Function[n, Plus @@ Map[#/EulerPhi[#] &, DeleteCases[Divisors[n], 1 | n]]], 3000], Positive[#] && IntegerQ[#] &]
%t Select[Table[Total[#/EulerPhi[#]&/@Most[Rest[Divisors[n]]]],{n,2,3000}],Positive[ #]&&IntegerQ[#]&] (* _Harvey P. Dale_, Oct 31 2020 *)
%t s[n_] := DivisorSum[n, #/EulerPhi[#] &, 1 < # < n &]; Select[s /@ Select[Range[10^4], CompositeQ], IntegerQ] (* _Amiram Eldar_, Jul 01 2022 *)
%Y Cf. A000010, A239886.
%Y Cf. A023898, A023899 for the versions with all divisors included.
%K nonn
%O 1,1
%A _Olivier Gérard_, Mar 29 2014
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