%I #9 Jul 29 2017 11:47:04
%S 0,2,1,6,0,11,1,11,5,17,-4,27,4,15,9,30,-3,38,-2,31,18,35,-12,54,15,
%T 29,12,55,-12,71,1,48,28,41,-7,90,16,43,6,89,-12,95,4,51,52,71,-28,
%U 116,14,72,26,97,-12,103,8,97,48,89,-48,167,28,55,41,108,6,143,10,99,22,143
%N First differences of A024816.
%C A024816(n) is the sum of the non-divisors k of n for k=2,3,...,n-1.
%C It appears that (1) a(n) = A120444(n)+1 if and only if n is a prime, (2) if a(n)<0 then A120444(n)<0, and (3) a(n)<=0 whenever n is of the form 6k-1. Are these conjectures easy to prove/disprove? (A120444 is the first difference of A004125 Sum of remainders of n mod k, for k = 1,2,3,...,n).
%H G. C. Greubel, <a href="/A163553/b163553.txt">Table of n, a(n) for n = 1..1000</a>
%t Differences[Table[Total[Complement[Range[n],Divisors[n]]],{n,80}]] (* _Harvey P. Dale_, Mar 05 2013 *)
%o (PARI) a(n) = n + 1 + sigma(n) - sigma(n+1); \\ _Michel Marcus_, Jul 29 2017
%Y Cf. A004125, A024816, A120444.
%K sign
%O 1,2
%A _John W. Layman_, Jul 30 2009