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Anti-divisor class sums of n.
1

%I #8 Jun 24 2014 01:08:18

%S 0,0,0,-1,1,0,-2,2,0,-2,2,-1,-1,2,0,-2,0,2,-2,2,0,-4,4,-1,-1,2,-2,0,2,

%T 0,-4,2,2,-2,2,0,-4,2,2,-3,3,-2,0,2,-2,0,0,2,-4,4,0,-6,6,0,-2,2,-2,-2,

%U 2,1,-1,0,2,-2,2,-2,-4,6,0,-2,0,0,-2,4,0,-4,2,2,-2,0,2,-6,6,-1,-3,4,-4,2,2,0,-2,0,0,-4,6,0,-6,6,0,-2,0,0,-2

%N Anti-divisor class sums of n.

%C An anti-divisor of n is an integer d in [2,n-1] such that n == (d-1)/2, d/2, or (d+1)/2 (mod d), the class of d being -1, 0, or 1, respectively. The class sum of n is the sum of the classes of all of its anti-divisors.

%C See A066272 for definition of anti-divisor.

%H Jon Perry, <a href="http://www.users.globalnet.co.uk/~perry/maths/antidivisorother2.htm">Class sums</a>

%F f(n)=sum(ad class)

%e The ad's of 10 are 3, 4 and 7, with classes -1, 0 and -1, so f(10)=-2.

%t a[n_ ] := Sum[Which[Mod[n, d]==(d-1)/2, -1, Mod[n, d]==(d+1)/2, 1, True, 0], {d, 2, n-1}]

%Y Cf. A066519.

%K sign

%O 1,7

%A _Jon Perry_, Jan 06 2002

%E Edited by _Dean Hickerson_, Jan 17 2002