A060794 - OEIS

%I #18 Jul 03 2018 02:34:40

%S 1,2,1,4,1,6,2,2,3,10,1,12,5,2,2,16,3,18,1,4,9,22,2,4,11,6,3,28,1,30,

%T 4,8,15,2,2,36,17,10,3,40,1,42,7,4,21,46,2,6,5,14,9,52,3,6,1,16,27,58,

%U 4,60,29,2,4,8,5,66,13,20,3,70,1,72,35,10,15,4,7,78,2,6,39,82,5,12,41,26

%N Difference between upper and lower central divisors of n.

%H Harry J. Smith, <a href="/A060794/b060794.txt">Table of n, a(n) for n = 2..1000</a>

%e Difference between upper and lower central divisors may be small or relatively large. So neither A060775 nor A033677 are always good central divisors as to their magnitude. n=182,D={1,2,7,13,14,26,91,182}; central divisors={13,14}, difference=1. n=254, D={1,2,127,254}, central divisors={2,127}, a(254)=125. n=p, D={1,p}. Here the central divisors are also marginal ones: a(p)=p-1.

%t a(n)=Part[Divisors[n], 1+cd[n]]-Part[Divisors[n], cd[n]], where cd[x_] := cd[x_] := Floor[DivisorSigma[0, x]/2]

%o (PARI) a(n)={my(d=divisors(n)); if(n>1, d[1 + #d\2] - d[#d\2], 0)} \\ _Harry J. Smith_, Jul 12 2009

%Y a(n) = A033677(n) - A060775(n).

%Y Cf. A060775, A060776, A060777, A033677, A000196.

%K nonn

%O 2,2

%A _Labos Elemer_, Apr 27 2001