%I
%S 0,1,2,1,4,5,6,5,8,9,10,5,12,13,14,13,16,17,18,5,20,21,22,17,24,25,26,
%T 5,28,17,30,29,32,33,34,17,36,37,38,29,40,41,42,5,44,45,46,41,48,49,
%U 50,5,52,53,54,45,56,57,58,33,60,61,62,61,64,65,66,5,68,57,70,57,72,73,74
%N Absolute value of difference between the even and odd first differences of the divisors of n.
%H Robert Israel, <a href="/A058359/b058359.txt">Table of n, a(n) for n = 1..10000</a>
%e The divisors of twelve are {1, 2, 3, 4, 6 and 12}, the first difference is {1, 1, 1, 2 and 6}. The even differences add up to 8 while the odd differences add up to 3. The absolute difference between the even and odd first differences of 12 therefore is 5.
%p f:= proc(n) local Q, evens,odds;
%p Q:= sort(convert(numtheory:divisors(n),list));
%p evens,odds:= selectremove(type,Q[2..1]Q[1..2],even);
%p abs(convert(evens,`+`)convert(odds,`+`))
%p end proc:
%p map(f, [$1..100]); # _Robert Israel_, Jul 05 2016
%t f[ n_Integer ] := (d = Divisors[ n ]; l = Length[ d ]; s = 0; i = 1; While[ i < l, e = d[ [ i + 1 ] ]  d[ [ i ] ]; If[ EvenQ[ e ], s = s + e, s = s  e ]; i++ ]; Abs[ s ]); Table[ f[ n ], {n, 1, 75} ]
%t avd[n_]:=Module[{d=Differences[Divisors[n]]},Abs[Total[Select[d,OddQ]]Total[ Select[ d,EvenQ]]]]; Array[avd,80] (* _Harvey P. Dale_, Dec 31 2018 *)
%K nonn
%O 1,3
%A _Robert G. Wilson v_, Dec 16 2000
