cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A239887 Integer values of the proper divisor balance of composite numbers.

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