%I #14 Feb 12 2017 14:39:58
%S -1,1,-3,2,3,5,3,-4,7,8,5,6,11,12,-15,14,5,14,13,19,19,20,19,-6,19,22,
%T 21,24,27,29,25,30,31,32,23,18,33,32,35,34,39,32,37,32,43,44,17,30,19,
%U 48,45,50,49,52,51,52,53,54,53,30,59,50,-63,58,63,50,61,66,67,68,59,36,55,44,69,74,71,74,49,70,75,76,77,82,75,82,83
%N a(n) = n - A006530(A000203(n)), difference between n and largest prime factor of the sum of its divisors.
%C Terms are mostly positive. At cases when sigma(n) is prime the differences are negative. See A071167.
%H Robert Israel, <a href="/A071166/b071166.txt">Table of n, a(n) for n = 2..10000</a>
%e n=12, divisors={1,2,3,4,6,12}, sigma(12)=28, its largest prime factor is 7, so a(12)=12-7=5.
%p gpf:= n -> max(numtheory:-factorset(n)):
%p seq(n - gpf(numtheory:-sigma(n)), n=2..100); # _Robert Israel_, Feb 12 2017
%t ma[x_] := Part[Reverse[Flatten[FactorInteger[x]]], 2] t=Table[w-ma[DivisorSigma[1, w]], {w, 2, 128}]
%o (PARI) a(n)=n-factor(sigma(n))[1,1] \\ _Charles R Greathouse IV_, Feb 19 2013
%Y Cf. A000203, A006530, A062700, A023194, A071167.
%K sign
%O 2,3
%A _Labos Elemer_, May 15 2002